{
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""
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"# Solving Differential Equations with Deep Learning\n",
"\n",
"The Universal Approximation Theorem states that a neural network can\n",
"approximate any function at a single hidden layer along with one input\n",
"and output layer to any given precision. \n",
"\n",
"An ordinary differential equation (ODE) is an equation involving functions having one variable.\n",
"\n",
"In general, an ordinary differential equation looks like"
]
},
{
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"id": "ac838a12",
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{ode} \\tag{1}\n",
"f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right) = 0\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ccee4286",
"metadata": {
"editable": true
},
"source": [
"where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n",
"\n",
"The $f\\left(x, g(x), g'(x), g''(x), \\, \\dots \\, , g^{(n)}(x)\\right)$ is just a way to write that there is an expression involving $x$ and $g(x), \\ g'(x), \\ g''(x), \\, \\dots \\, , \\text{ and } g^{(n)}(x)$ on the left side of the equality sign in ([1](#ode)).\n",
"The highest order of derivative, that is the value of $n$, determines to the order of the equation.\n",
"The equation is referred to as a $n$-th order ODE.\n",
"Along with ([1](#ode)), some additional conditions of the function $g(x)$ are typically given\n",
"for the solution to be unique.\n",
"\n",
"Let the trial solution $g_t(x)$ be"
]
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"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"\tg_t(x) = h_1(x) + h_2(x,N(x,P))\n",
"\\label{_auto1} \\tag{2}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "74f33170",
"metadata": {
"editable": true
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"source": [
"where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n",
"of conditions, $N(x,P)$ a neural network with weights and biases\n",
"described by $P$ and $h_2(x, N(x,P))$ some expression involving the\n",
"neural network. The role of the function $h_2(x, N(x,P))$, is to\n",
"ensure that the output from $N(x,P)$ is zero when $g_t(x)$ is\n",
"evaluated at the values of $x$ where the given conditions must be\n",
"satisfied. The function $h_1(x)$ should alone make $g_t(x)$ satisfy\n",
"the conditions.\n",
"\n",
"But what about the network $N(x,P)$?\n",
"\n",
"As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation.\n",
"\n",
"For the minimization to be defined, we need to have a cost function at hand to minimize.\n",
"\n",
"It is given that $f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)$ should be equal to zero in ([1](#ode)).\n",
"We can choose to consider the mean squared error as the cost function for an input $x$.\n",
"Since we are looking at one input, the cost function is just $f$ squared.\n",
"The cost function $c\\left(x, P \\right)$ can therefore be expressed as"
]
},
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"id": "2565ab16",
"metadata": {
"editable": true
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"source": [
"$$\n",
"C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "83d4ee25",
"metadata": {
"editable": true
},
"source": [
"If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n",
"the cost function becomes"
]
},
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"id": "a7a3a709",
"metadata": {
"editable": true
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{cost} \\tag{3}\n",
"\tC\\left(\\boldsymbol{x}, P\\right) = \\frac{1}{N} \\sum_{i=1}^N \\big(f\\left(x_i, \\, g(x_i), \\, g'(x_i), \\, g''(x_i), \\, \\dots \\, , \\, g^{(n)}(x_i)\\right)\\big)^2\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "d3ca8026",
"metadata": {
"editable": true
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"source": [
"The neural net should then find the parameters $P$ that minimizes the cost function in\n",
"([3](#cost)) for a set of $N$ training samples $x_i$.\n",
"\n",
"To perform the minimization using gradient descent, the gradient of $C\\left(\\boldsymbol{x}, P\\right)$ is needed.\n",
"It might happen so that finding an analytical expression of the gradient of $C(\\boldsymbol{x}, P)$ from ([3](#cost)) gets too messy, depending on which cost function one desires to use.\n",
"\n",
"Luckily, there exists libraries that makes the job for us through automatic differentiation.\n",
"Automatic differentiation is a method of finding the derivatives numerically with very high precision."
]
},
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"cell_type": "markdown",
"id": "9bde4bd4",
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"### Example: Exponential decay\n",
"\n",
"An exponential decay of a quantity $g(x)$ is described by the equation"
]
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"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{solve_expdec} \\tag{4}\n",
" g'(x) = -\\gamma g(x)\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "273549a4",
"metadata": {
"editable": true
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"with $g(0) = g_0$ for some chosen initial value $g_0$.\n",
"\n",
"The analytical solution of ([4](#solve_expdec)) is"
]
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"id": "db3c6623",
"metadata": {
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"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation}\n",
" g(x) = g_0 \\exp\\left(-\\gamma x\\right)\n",
"\\label{_auto2} \\tag{5}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "8547e3c8",
"metadata": {
"editable": true
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"source": [
"Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec)).\n",
"\n",
"The program will use a neural network to solve"
]
},
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"metadata": {
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"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{solveode} \\tag{6}\n",
"g'(x) = -\\gamma g(x)\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "d25b1e02",
"metadata": {
"editable": true
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"source": [
"where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n",
"\n",
"In this example, $\\gamma = 2$ and $g_0 = 10$.\n",
"\n",
"To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be"
]
},
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"id": "7c5dd91e",
"metadata": {
"editable": true
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"source": [
"$$\n",
"g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "24223062",
"metadata": {
"editable": true
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"source": [
"with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer.\n",
"\n",
"In this network, there are no weights and bias at the input layer, so $P = \\{ P_{\\text{hidden}}, P_{\\text{output}} \\}$.\n",
"If there are $N_{\\text{hidden} }$ neurons in the hidden layer, then $P_{\\text{hidden}}$ is a $N_{\\text{hidden} } \\times (1 + N_{\\text{input}})$ matrix, given that there are $N_{\\text{input}}$ neurons in the input layer.\n",
"\n",
"The first column in $P_{\\text{hidden} }$ represents the bias for each neuron in the hidden layer and the second column represents the weights for each neuron in the hidden layer from the input layer.\n",
"If there are $N_{\\text{output} }$ neurons in the output layer, then $P_{\\text{output}} $ is a $N_{\\text{output} } \\times (1 + N_{\\text{hidden} })$ matrix.\n",
"\n",
"Its first column represents the bias of each neuron and the remaining columns represents the weights to each neuron.\n",
"\n",
"It is given that $g(0) = g_0$. The trial solution must fulfill this condition to be a proper solution of ([6](#solveode)). A possible way to ensure that $g_t(0, P) = g_0$, is to let $F(N(x,P)) = x \\cdot N(x,P)$ and $A(x) = g_0$. This gives the following trial solution:"
]
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{trial} \\tag{7}\n",
"g_t(x, P) = g_0 + x \\cdot N(x, P)\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ea4a0013",
"metadata": {
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"source": [
"### Reformulating the problem\n",
"\n",
"We wish that our neural network manages to minimize a given cost function.\n",
"\n",
"A reformulation of out equation, ([6](#solveode)), must therefore be done,\n",
"such that it describes the problem a neural network can solve for.\n",
"\n",
"The neural network must find the set of weights and biases $P$ such that the trial solution in ([7](#trial)) satisfies ([6](#solveode)).\n",
"\n",
"The trial solution"
]
},
{
"cell_type": "markdown",
"id": "2351b84f",
"metadata": {
"editable": true
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"source": [
"$$\n",
"g_t(x, P) = g_0 + x \\cdot N(x, P)\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "f6cc00e4",
"metadata": {
"editable": true
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"source": [
"has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that"
]
},
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"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{nnmin} \\tag{8}\n",
"g_t'(x, P) = - \\gamma g_t(x, P)\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "feff9ab3",
"metadata": {
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"source": [
"is fulfilled as *best as possible*.\n",
"\n",
"The left hand side and right hand side of ([8](#nnmin)) must be computed separately, and then the neural network must choose weights and biases, contained in $P$, such that the sides are equal as best as possible.\n",
"This means that the absolute or squared difference between the sides must be as close to zero, ideally equal to zero.\n",
"In this case, the difference squared shows to be an appropriate measurement of how erroneous the trial solution is with respect to $P$ of the neural network.\n",
"\n",
"This gives the following cost function our neural network must solve for:"
]
},
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"id": "0c6f0e79",
"metadata": {
"editable": true
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"source": [
"$$\n",
"\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "9302a1dd",
"metadata": {
"editable": true
},
"source": [
"(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n",
"\n",
"or, in terms of weights and biases for the hidden and output layer in our network:"
]
},
{
"cell_type": "markdown",
"id": "f7f204bb",
"metadata": {
"editable": true
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"source": [
"$$\n",
"\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "8d61d75f",
"metadata": {
"editable": true
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"source": [
"for an input value $x$.\n",
"\n",
"If the neural network evaluates $g_t(x, P)$ at more values for $x$, say $N$ values $x_i$ for $i = 1, \\dots, N$, then the *total* error to minimize becomes"
]
},
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"metadata": {
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{min} \\tag{9}\n",
"\\min_{P}\\Big\\{\\frac{1}{N} \\sum_{i=1}^N \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2 \\Big\\}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "5e296388",
"metadata": {
"editable": true
},
"source": [
"Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes"
]
},
{
"cell_type": "markdown",
"id": "fe010d79",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\min_{P} C(\\boldsymbol{x}, P)\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "add715f9",
"metadata": {
"editable": true
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"source": [
"In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n",
"\n",
"$$\n",
"\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }} C(\\boldsymbol{x}, \\{P_{\\text{hidden} }, P_{\\text{output} }\\})\n",
"$$\n",
"\n",
"For simplicity, it is assumed that the input is an array $\\boldsymbol{x} = (x_1, \\dots, x_N)$ with $N$ elements. It is at these points the neural network should find $P$ such that it fulfills ([9](#min)).\n",
"\n",
"First, the neural network must feed forward the inputs.\n",
"This means that $\\boldsymbol{x}s$ must be passed through an input layer, a hidden layer and a output layer. The input layer in this case, does not need to process the data any further.\n",
"The input layer will consist of $N_{\\text{input} }$ neurons, passing its element to each neuron in the hidden layer. The number of neurons in the hidden layer will be $N_{\\text{hidden} }$.\n",
"\n",
"For the $i$-th in the hidden layer with weight $w_i^{\\text{hidden} }$ and bias $b_i^{\\text{hidden} }$, the weighting from the $j$-th neuron at the input layer is:"
]
},
{
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"id": "cb9b22eb",
"metadata": {
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"source": [
"$$\n",
"\\begin{aligned}\n",
"z_{i,j}^{\\text{hidden}} &= b_i^{\\text{hidden}} + w_i^{\\text{hidden}}x_j \\\\\n",
"&=\n",
"\\begin{pmatrix}\n",
"b_i^{\\text{hidden}} & w_i^{\\text{hidden}}\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"1 \\\\\n",
"x_j\n",
"\\end{pmatrix}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "49f3c493",
"metadata": {
"editable": true
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"source": [
"The result after weighting the inputs at the $i$-th hidden neuron can be written as a vector:"
]
},
{
"cell_type": "markdown",
"id": "a352bd61",
"metadata": {
"editable": true
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"source": [
"$$\n",
"\\begin{aligned}\n",
"\\boldsymbol{z}_{i}^{\\text{hidden}} &= \\Big( b_i^{\\text{hidden}} + w_i^{\\text{hidden}}x_1 , \\ b_i^{\\text{hidden}} + w_i^{\\text{hidden}} x_2, \\ \\dots \\, , \\ b_i^{\\text{hidden}} + w_i^{\\text{hidden}} x_N\\Big) \\\\\n",
"&=\n",
"\\begin{pmatrix}\n",
" b_i^{\\text{hidden}} & w_i^{\\text{hidden}}\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"1 & 1 & \\dots & 1 \\\\\n",
"x_1 & x_2 & \\dots & x_N\n",
"\\end{pmatrix} \\\\\n",
"&= \\boldsymbol{p}_{i, \\text{hidden}}^T X\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "e5636ad7",
"metadata": {
"editable": true
},
"source": [
"The vector $\\boldsymbol{p}_{i, \\text{hidden}}^T$ constitutes each row in $P_{\\text{hidden} }$, which contains the weights for the neural network to minimize according to ([9](#min)).\n",
"\n",
"After having found $\\boldsymbol{z}_{i}^{\\text{hidden}} $ for every $i$-th neuron within the hidden layer, the vector will be sent to an activation function $a_i(\\boldsymbol{z})$.\n",
"\n",
"In this example, the sigmoid function has been chosen to be the activation function for each hidden neuron:"
]
},
{
"cell_type": "markdown",
"id": "68bb8b9c",
"metadata": {
"editable": true
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"source": [
"$$\n",
"f(z) = \\frac{1}{1 + \\exp{(-z)}}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ff6e6536",
"metadata": {
"editable": true
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"source": [
"It is possible to use other activations functions for the hidden layer also.\n",
"\n",
"The output $\\boldsymbol{x}_i^{\\text{hidden}}$ from each $i$-th hidden neuron is:\n",
"\n",
"$$\n",
"\\boldsymbol{x}_i^{\\text{hidden} } = f\\big( \\boldsymbol{z}_{i}^{\\text{hidden}} \\big)\n",
"$$\n",
"\n",
"The outputs $\\boldsymbol{x}_i^{\\text{hidden} } $ are then sent to the output layer.\n",
"\n",
"The output layer consists of one neuron in this case, and combines the\n",
"output from each of the neurons in the hidden layers. The output layer\n",
"combines the results from the hidden layer using some weights $w_i^{\\text{output}}$\n",
"and biases $b_i^{\\text{output}}$. In this case,\n",
"it is assumes that the number of neurons in the output layer is one.\n",
"\n",
"The procedure of weighting the output neuron $j$ in the hidden layer to the $i$-th neuron in the output layer is similar as for the hidden layer described previously."
]
},
{
"cell_type": "markdown",
"id": "6fb4c55b",
"metadata": {
"editable": true
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"source": [
"$$\n",
"\\begin{aligned}\n",
"z_{1,j}^{\\text{output}} & =\n",
"\\begin{pmatrix}\n",
"b_1^{\\text{output}} & \\boldsymbol{w}_1^{\\text{output}}\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"1 \\\\\n",
"\\boldsymbol{x}_j^{\\text{hidden}}\n",
"\\end{pmatrix}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "09c31d8d",
"metadata": {
"editable": true
},
"source": [
"Expressing $z_{1,j}^{\\text{output}}$ as a vector gives the following way of weighting the inputs from the hidden layer:"
]
},
{
"cell_type": "markdown",
"id": "f81fe361",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\boldsymbol{z}_{1}^{\\text{output}} =\n",
"\\begin{pmatrix}\n",
"b_1^{\\text{output}} & \\boldsymbol{w}_1^{\\text{output}}\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"1 & 1 & \\dots & 1 \\\\\n",
"\\boldsymbol{x}_1^{\\text{hidden}} & \\boldsymbol{x}_2^{\\text{hidden}} & \\dots & \\boldsymbol{x}_N^{\\text{hidden}}\n",
"\\end{pmatrix}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "c309a4ce",
"metadata": {
"editable": true
},
"source": [
"In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network.\n",
"\n",
"The next step is to decide how the parameters should be changed such that they minimize the cost function.\n",
"\n",
"The chosen cost function for this problem is"
]
},
{
"cell_type": "markdown",
"id": "ea47ae29",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "9dd83767",
"metadata": {
"editable": true
},
"source": [
"In order to minimize the cost function, an optimization method must be chosen.\n",
"\n",
"Here, gradient descent with a constant step size has been chosen."
]
},
{
"cell_type": "markdown",
"id": "531a7b4f",
"metadata": {
"editable": true
},
"source": [
"### Gradient descent\n",
"\n",
"The idea of the gradient descent algorithm is to update parameters in\n",
"a direction where the cost function decreases goes to a minimum.\n",
"\n",
"In general, the update of some parameters $\\boldsymbol{\\omega}$ given a cost\n",
"function defined by some weights $\\boldsymbol{\\omega}$, $C(\\boldsymbol{x},\n",
"\\boldsymbol{\\omega})$, goes as follows:"
]
},
{
"cell_type": "markdown",
"id": "e10c204a",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "9f4fa48e",
"metadata": {
"editable": true
},
"source": [
"for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n",
"\n",
"The value of $\\lambda$ decides how large steps the algorithm must take\n",
"in the direction of $ \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})$.\n",
"The notation $\\nabla_{\\boldsymbol{\\omega}}$ express the gradient with respect\n",
"to the elements in $\\boldsymbol{\\omega}$.\n",
"\n",
"In our case, we have to minimize the cost function $C(\\boldsymbol{x}, P)$ with\n",
"respect to the two sets of weights and biases, that is for the hidden\n",
"layer $P_{\\text{hidden} }$ and for the output layer $P_{\\text{output}\n",
"}$ .\n",
"\n",
"This means that $P_{\\text{hidden} }$ and $P_{\\text{output} }$ is updated by"
]
},
{
"cell_type": "markdown",
"id": "4652fc79",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{aligned}\n",
"P_{\\text{hidden},\\text{new}} &= P_{\\text{hidden}} - \\lambda \\nabla_{P_{\\text{hidden}}} C(\\boldsymbol{x}, P) \\\\\n",
"P_{\\text{output},\\text{new}} &= P_{\\text{output}} - \\lambda \\nabla_{P_{\\text{output}}} C(\\boldsymbol{x}, P)\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "41ae0626",
"metadata": {
"editable": true
},
"source": [
"### The code for solving the ODE"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "af7c165f",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 367.01\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost: 0.0666807\n",
"Max absolute difference: 0.0437499\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_50_2.png"
}
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"import autograd.numpy as np\n",
"from autograd import grad, elementwise_grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import pyplot as plt\n",
"\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"# Assuming one input, hidden, and output layer\n",
"def neural_network(params, x):\n",
"\n",
" # Find the weights (including and biases) for the hidden and output layer.\n",
" # Assume that params is a list of parameters for each layer.\n",
" # The biases are the first element for each array in params,\n",
" # and the weights are the remaning elements in each array in params.\n",
"\n",
" w_hidden = params[0]\n",
" w_output = params[1]\n",
"\n",
" # Assumes input x being an one-dimensional array\n",
" num_values = np.size(x)\n",
" x = x.reshape(-1, num_values)\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
"\n",
" ## Hidden layer:\n",
"\n",
" # Add a row of ones to include bias\n",
" x_input = np.concatenate((np.ones((1,num_values)), x_input ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_input)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" ## Output layer:\n",
"\n",
" # Include bias:\n",
" x_hidden = np.concatenate((np.ones((1,num_values)), x_hidden ), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_hidden)\n",
" x_output = z_output\n",
"\n",
" return x_output\n",
"\n",
"# The trial solution using the deep neural network:\n",
"def g_trial(x,params, g0 = 10):\n",
" return g0 + x*neural_network(params,x)\n",
"\n",
"# The right side of the ODE:\n",
"def g(x, g_trial, gamma = 2):\n",
" return -gamma*g_trial\n",
"\n",
"# The cost function:\n",
"def cost_function(P, x):\n",
"\n",
" # Evaluate the trial function with the current parameters P\n",
" g_t = g_trial(x,P)\n",
"\n",
" # Find the derivative w.r.t x of the neural network\n",
" d_net_out = elementwise_grad(neural_network,1)(P,x)\n",
"\n",
" # Find the derivative w.r.t x of the trial function\n",
" d_g_t = elementwise_grad(g_trial,0)(x,P)\n",
"\n",
" # The right side of the ODE\n",
" func = g(x, g_t)\n",
"\n",
" err_sqr = (d_g_t - func)**2\n",
" cost_sum = np.sum(err_sqr)\n",
"\n",
" return cost_sum / np.size(err_sqr)\n",
"\n",
"# Solve the exponential decay ODE using neural network with one input, hidden, and output layer\n",
"def solve_ode_neural_network(x, num_neurons_hidden, num_iter, lmb):\n",
" ## Set up initial weights and biases\n",
"\n",
" # For the hidden layer\n",
" p0 = npr.randn(num_neurons_hidden, 2 )\n",
"\n",
" # For the output layer\n",
" p1 = npr.randn(1, num_neurons_hidden + 1 ) # +1 since bias is included\n",
"\n",
" P = [p0, p1]\n",
"\n",
" print('Initial cost: %g'%cost_function(P, x))\n",
"\n",
" ## Start finding the optimal weights using gradient descent\n",
"\n",
" # Find the Python function that represents the gradient of the cost function\n",
" # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer\n",
" cost_function_grad = grad(cost_function,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" # Evaluate the gradient at the current weights and biases in P.\n",
" # The cost_grad consist now of two arrays;\n",
" # one for the gradient w.r.t P_hidden and\n",
" # one for the gradient w.r.t P_output\n",
" cost_grad = cost_function_grad(P, x)\n",
"\n",
" P[0] = P[0] - lmb * cost_grad[0]\n",
" P[1] = P[1] - lmb * cost_grad[1]\n",
"\n",
" print('Final cost: %g'%cost_function(P, x))\n",
"\n",
" return P\n",
"\n",
"def g_analytic(x, gamma = 2, g0 = 10):\n",
" return g0*np.exp(-gamma*x)\n",
"\n",
"# Solve the given problem\n",
"if __name__ == '__main__':\n",
" # Set seed such that the weight are initialized\n",
" # with same weights and biases for every run.\n",
" npr.seed(15)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" N = 10\n",
" x = np.linspace(0, 1, N)\n",
"\n",
" ## Set up the initial parameters\n",
" num_hidden_neurons = 10\n",
" num_iter = 10000\n",
" lmb = 0.001\n",
"\n",
" # Use the network\n",
" P = solve_ode_neural_network(x, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" # Print the deviation from the trial solution and true solution\n",
" res = g_trial(x,P)\n",
" res_analytical = g_analytic(x)\n",
"\n",
" print('Max absolute difference: %g'%np.max(np.abs(res - res_analytical)))\n",
"\n",
" # Plot the results\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.title('Performance of neural network solving an ODE compared to the analytical solution')\n",
" plt.plot(x, res_analytical)\n",
" plt.plot(x, res[0,:])\n",
" plt.legend(['analytical','nn'])\n",
" plt.xlabel('x')\n",
" plt.ylabel('g(x)')\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "875a0c0b",
"metadata": {
"editable": true
},
"source": [
"## The network with one input layer, specified number of hidden layers, and one output layer\n",
"\n",
"It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.\n",
"\n",
"The number of neurons within each hidden layer are given as a list of integers in the program below."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "00684827",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 324.246\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
" return asarray(a).size\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost: 0.119936\n"
]
},
{
"data": {
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"text/plain": [
""
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"source": [
"import autograd.numpy as np\n",
"from autograd import grad, elementwise_grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import pyplot as plt\n",
"\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"# The neural network with one input layer and one output layer,\n",
"# but with number of hidden layers specified by the user.\n",
"def deep_neural_network(deep_params, x):\n",
" # N_hidden is the number of hidden layers\n",
"\n",
" N_hidden = np.size(deep_params) - 1 # -1 since params consists of\n",
" # parameters to all the hidden\n",
" # layers AND the output layer.\n",
"\n",
" # Assumes input x being an one-dimensional array\n",
" num_values = np.size(x)\n",
" x = x.reshape(-1, num_values)\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
"\n",
" # Due to multiple hidden layers, define a variable referencing to the\n",
" # output of the previous layer:\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = deep_params[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = deep_params[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output\n",
"\n",
"# The trial solution using the deep neural network:\n",
"def g_trial_deep(x,params, g0 = 10):\n",
" return g0 + x*deep_neural_network(params, x)\n",
"\n",
"# The right side of the ODE:\n",
"def g(x, g_trial, gamma = 2):\n",
" return -gamma*g_trial\n",
"\n",
"# The same cost function as before, but calls deep_neural_network instead.\n",
"def cost_function_deep(P, x):\n",
"\n",
" # Evaluate the trial function with the current parameters P\n",
" g_t = g_trial_deep(x,P)\n",
"\n",
" # Find the derivative w.r.t x of the neural network\n",
" d_net_out = elementwise_grad(deep_neural_network,1)(P,x)\n",
"\n",
" # Find the derivative w.r.t x of the trial function\n",
" d_g_t = elementwise_grad(g_trial_deep,0)(x,P)\n",
"\n",
" # The right side of the ODE\n",
" func = g(x, g_t)\n",
"\n",
" err_sqr = (d_g_t - func)**2\n",
" cost_sum = np.sum(err_sqr)\n",
"\n",
" return cost_sum / np.size(err_sqr)\n",
"\n",
"# Solve the exponential decay ODE using neural network with one input and one output layer,\n",
"# but with specified number of hidden layers from the user.\n",
"def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
" # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
"\n",
" # The number of elements in the list num_hidden_neurons thus represents\n",
" # the number of hidden layers.\n",
"\n",
" # Find the number of hidden layers:\n",
" N_hidden = np.size(num_neurons)\n",
"\n",
" ## Set up initial weights and biases\n",
"\n",
" # Initialize the list of parameters:\n",
" P = [None]*(N_hidden + 1) # + 1 to include the output layer\n",
"\n",
" P[0] = npr.randn(num_neurons[0], 2 )\n",
" for l in range(1,N_hidden):\n",
" P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias\n",
"\n",
" # For the output layer\n",
" P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included\n",
"\n",
" print('Initial cost: %g'%cost_function_deep(P, x))\n",
"\n",
" ## Start finding the optimal weights using gradient descent\n",
"\n",
" # Find the Python function that represents the gradient of the cost function\n",
" # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer\n",
" cost_function_deep_grad = grad(cost_function_deep,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" # Evaluate the gradient at the current weights and biases in P.\n",
" # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases\n",
" # in the hidden layers and output layers evaluated at x.\n",
" cost_deep_grad = cost_function_deep_grad(P, x)\n",
"\n",
" for l in range(N_hidden+1):\n",
" P[l] = P[l] - lmb * cost_deep_grad[l]\n",
"\n",
" print('Final cost: %g'%cost_function_deep(P, x))\n",
"\n",
" return P\n",
"\n",
"def g_analytic(x, gamma = 2, g0 = 10):\n",
" return g0*np.exp(-gamma*x)\n",
"\n",
"# Solve the given problem\n",
"if __name__ == '__main__':\n",
" npr.seed(15)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" N = 10\n",
" x = np.linspace(0, 1, N)\n",
"\n",
" ## Set up the initial parameters\n",
" num_hidden_neurons = np.array([10,10])\n",
" num_iter = 10000\n",
" lmb = 0.001\n",
"\n",
" P = solve_ode_deep_neural_network(x, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" res = g_trial_deep(x,P)\n",
" res_analytical = g_analytic(x)\n",
"\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.title('Performance of a deep neural network solving an ODE compared to the analytical solution')\n",
" plt.plot(x, res_analytical)\n",
" plt.plot(x, res[0,:])\n",
" plt.legend(['analytical','dnn'])\n",
" plt.ylabel('g(x)')\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "5420c490",
"metadata": {
"editable": true
},
"source": [
"### Example: Population growth\n",
"\n",
"A logistic model of population growth assumes that a population converges toward an equilibrium.\n",
"The population growth can be modeled by"
]
},
{
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"id": "1436ed3c",
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{log} \\tag{10}\n",
"\tg'(t) = \\alpha g(t)(A - g(t))\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "a590bdb6",
"metadata": {
"editable": true
},
"source": [
"where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n",
"Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n",
"\n",
"In this example, similar network as for the exponential decay using Autograd has been used to solve the equation. However, as the implementation might suffer from e.g numerical instability\n",
"and high execution time (this might be more apparent in the examples solving PDEs),\n",
"using a library like TensorFlow is recommended.\n",
"Here, we stay with a more simple approach and implement for comparison, the simple forward Euler method.\n",
"\n",
"Here, we will model a population $g(t)$ in an environment having carrying capacity $A$.\n",
"The population follows the model"
]
},
{
"cell_type": "markdown",
"id": "48d788d6",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{solveode_population} \\tag{11}\n",
"g'(t) = \\alpha g(t)(A - g(t))\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "169c6c25",
"metadata": {
"editable": true
},
"source": [
"where $g(0) = g_0$.\n",
"\n",
"In this example, we let $\\alpha = 2$, $A = 1$, and $g_0 = 1.2$.\n",
"\n",
"We will get a slightly different trial solution, as the boundary conditions are different\n",
"compared to the case for exponential decay.\n",
"\n",
"A possible trial solution satisfying the condition $g(0) = g_0$ could be\n",
"\n",
"$$\n",
"h_1(t) = g_0 + t \\cdot N(t,P)\n",
"$$\n",
"\n",
"with $N(t,P)$ being the output from the neural network with weights and biases for each layer collected in the set $P$.\n",
"\n",
"The analytical solution is\n",
"\n",
"$$\n",
"g(t) = \\frac{Ag_0}{g_0 + (A - g_0)\\exp(-\\alpha A t)}\n",
"$$\n",
"\n",
"The network will be the similar as for the exponential decay example, but with some small modifications for our problem."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6d2e33bf",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 0.221805\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
" return asarray(a).size\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost: 0.000417932\n",
"The max absolute difference between the solutions is: 0.00424909\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_58_3.png"
}
},
"output_type": "display_data"
}
],
"source": [
"import autograd.numpy as np\n",
"from autograd import grad, elementwise_grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import pyplot as plt\n",
"\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"# Function to get the parameters.\n",
"# Done such that one can easily change the paramaters after one's liking.\n",
"def get_parameters():\n",
" alpha = 2\n",
" A = 1\n",
" g0 = 1.2\n",
" return alpha, A, g0\n",
"\n",
"def deep_neural_network(P, x):\n",
" # N_hidden is the number of hidden layers\n",
" N_hidden = np.size(P) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
"\n",
" # Assumes input x being an one-dimensional array\n",
" num_values = np.size(x)\n",
" x = x.reshape(-1, num_values)\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
"\n",
" # Due to multiple hidden layers, define a variable referencing to the\n",
" # output of the previous layer:\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = P[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = P[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output\n",
"\n",
"\n",
"def cost_function_deep(P, x):\n",
"\n",
" # Evaluate the trial function with the current parameters P\n",
" g_t = g_trial_deep(x,P)\n",
"\n",
" # Find the derivative w.r.t x of the trial function\n",
" d_g_t = elementwise_grad(g_trial_deep,0)(x,P)\n",
"\n",
" # The right side of the ODE\n",
" func = f(x, g_t)\n",
"\n",
" err_sqr = (d_g_t - func)**2\n",
" cost_sum = np.sum(err_sqr)\n",
"\n",
" return cost_sum / np.size(err_sqr)\n",
"\n",
"# The right side of the ODE:\n",
"def f(x, g_trial):\n",
" alpha,A, g0 = get_parameters()\n",
" return alpha*g_trial*(A - g_trial)\n",
"\n",
"# The trial solution using the deep neural network:\n",
"def g_trial_deep(x, params):\n",
" alpha,A, g0 = get_parameters()\n",
" return g0 + x*deep_neural_network(params,x)\n",
"\n",
"# The analytical solution:\n",
"def g_analytic(t):\n",
" alpha,A, g0 = get_parameters()\n",
" return A*g0/(g0 + (A - g0)*np.exp(-alpha*A*t))\n",
"\n",
"def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
" # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
"\n",
" # Find the number of hidden layers:\n",
" N_hidden = np.size(num_neurons)\n",
"\n",
" ## Set up initial weigths and biases\n",
"\n",
" # Initialize the list of parameters:\n",
" P = [None]*(N_hidden + 1) # + 1 to include the output layer\n",
"\n",
" P[0] = npr.randn(num_neurons[0], 2 )\n",
" for l in range(1,N_hidden):\n",
" P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias\n",
"\n",
" # For the output layer\n",
" P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included\n",
"\n",
" print('Initial cost: %g'%cost_function_deep(P, x))\n",
"\n",
" ## Start finding the optimal weigths using gradient descent\n",
"\n",
" # Find the Python function that represents the gradient of the cost function\n",
" # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer\n",
" cost_function_deep_grad = grad(cost_function_deep,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" # Evaluate the gradient at the current weights and biases in P.\n",
" # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases\n",
" # in the hidden layers and output layers evaluated at x.\n",
" cost_deep_grad = cost_function_deep_grad(P, x)\n",
"\n",
" for l in range(N_hidden+1):\n",
" P[l] = P[l] - lmb * cost_deep_grad[l]\n",
"\n",
" print('Final cost: %g'%cost_function_deep(P, x))\n",
"\n",
" return P\n",
"\n",
"if __name__ == '__main__':\n",
" npr.seed(4155)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" Nt = 10\n",
" T = 1\n",
" t = np.linspace(0,T, Nt)\n",
"\n",
" ## Set up the initial parameters\n",
" num_hidden_neurons = [100, 50, 25]\n",
" num_iter = 1000\n",
" lmb = 1e-3\n",
"\n",
" P = solve_ode_deep_neural_network(t, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" g_dnn_ag = g_trial_deep(t,P)\n",
" g_analytical = g_analytic(t)\n",
"\n",
" # Find the maximum absolute difference between the solutons:\n",
" diff_ag = np.max(np.abs(g_dnn_ag - g_analytical))\n",
" print(\"The max absolute difference between the solutions is: %g\"%diff_ag)\n",
"\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.title('Performance of neural network solving an ODE compared to the analytical solution')\n",
" plt.plot(t, g_analytical)\n",
" plt.plot(t, g_dnn_ag[0,:])\n",
" plt.legend(['analytical','nn'])\n",
" plt.xlabel('t')\n",
" plt.ylabel('g(t)')\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e31ec549",
"metadata": {
"editable": true
},
"source": [
"## Using forward Euler to solve the ODE\n",
"\n",
"A straightforward way of solving an ODE numerically, is to use Euler's method.\n",
"\n",
"Euler's method uses Taylor series to approximate the value at a function $f$ at a step $\\Delta x$ from $x$:\n",
"\n",
"$$\n",
"f(x + \\Delta x) \\approx f(x) + \\Delta x f'(x)\n",
"$$\n",
"\n",
"In our case, using Euler's method to approximate the value of $g$ at a step $\\Delta t$ from $t$ yields"
]
},
{
"cell_type": "markdown",
"id": "2e9ee105",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{aligned}\n",
" g(t + \\Delta t) &\\approx g(t) + \\Delta t g'(t) \\\\\n",
" &= g(t) + \\Delta t \\big(\\alpha g(t)(A - g(t))\\big)\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "e876da16",
"metadata": {
"editable": true
},
"source": [
"along with the condition that $g(0) = g_0$.\n",
"\n",
"Let $t_i = i \\cdot \\Delta t$ where $\\Delta t = \\frac{T}{N_t-1}$ where $T$ is the final time our solver must solve for and $N_t$ the number of values for $t \\in [0, T]$ for $i = 0, \\dots, N_t-1$.\n",
"\n",
"For $i \\geq 1$, we have that"
]
},
{
"cell_type": "markdown",
"id": "b79a3def",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{aligned}\n",
"t_i &= i\\Delta t \\\\\n",
"&= (i - 1)\\Delta t + \\Delta t \\\\\n",
"&= t_{i-1} + \\Delta t\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "9d99cb4e",
"metadata": {
"editable": true
},
"source": [
"Now, if $g_i = g(t_i)$ then"
]
},
{
"cell_type": "markdown",
"id": "3b9dcc24",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
" g_i &= g(t_i) \\\\\n",
" &= g(t_{i-1} + \\Delta t) \\\\\n",
" &\\approx g(t_{i-1}) + \\Delta t \\big(\\alpha g(t_{i-1})(A - g(t_{i-1}))\\big) \\\\\n",
" &= g_{i-1} + \\Delta t \\big(\\alpha g_{i-1}(A - g_{i-1})\\big)\n",
" \\end{aligned}\n",
"\\end{equation} \\label{odenum} \\tag{12}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "65ce688e",
"metadata": {
"editable": true
},
"source": [
"for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n",
"\n",
"Equation ([12](#odenum)) could be implemented in the following way,\n",
"extending the program that uses the network using Autograd:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d5497948",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 0.221805\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
" return asarray(a).size\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost: 0.000417932\n",
"The max absolute difference between the solutions is: 0.00424909\n",
"Max absolute difference between Euler method and analytical: 0.011225\n",
"Max absolute difference between deep neural network and analytical: 0.00424909\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_66_4.png"
}
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"output_type": "display_data"
}
],
"source": [
"# Assume that all function definitions from the example program using Autograd\n",
"# are located here.\n",
"\n",
"if __name__ == '__main__':\n",
" npr.seed(4155)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" Nt = 10\n",
" T = 1\n",
" t = np.linspace(0,T, Nt)\n",
"\n",
" ## Set up the initial parameters\n",
" num_hidden_neurons = [100,50,25]\n",
" num_iter = 1000\n",
" lmb = 1e-3\n",
"\n",
" P = solve_ode_deep_neural_network(t, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" g_dnn_ag = g_trial_deep(t,P)\n",
" g_analytical = g_analytic(t)\n",
"\n",
" # Find the maximum absolute difference between the solutons:\n",
" diff_ag = np.max(np.abs(g_dnn_ag - g_analytical))\n",
" print(\"The max absolute difference between the solutions is: %g\"%diff_ag)\n",
"\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.title('Performance of neural network solving an ODE compared to the analytical solution')\n",
" plt.plot(t, g_analytical)\n",
" plt.plot(t, g_dnn_ag[0,:])\n",
" plt.legend(['analytical','nn'])\n",
" plt.xlabel('t')\n",
" plt.ylabel('g(t)')\n",
"\n",
" ## Find an approximation to the funtion using forward Euler\n",
"\n",
" alpha, A, g0 = get_parameters()\n",
" dt = T/(Nt - 1)\n",
"\n",
" # Perform forward Euler to solve the ODE\n",
" g_euler = np.zeros(Nt)\n",
" g_euler[0] = g0\n",
"\n",
" for i in range(1,Nt):\n",
" g_euler[i] = g_euler[i-1] + dt*(alpha*g_euler[i-1]*(A - g_euler[i-1]))\n",
"\n",
" # Print the errors done by each method\n",
" diff1 = np.max(np.abs(g_euler - g_analytical))\n",
" diff2 = np.max(np.abs(g_dnn_ag[0,:] - g_analytical))\n",
"\n",
" print('Max absolute difference between Euler method and analytical: %g'%diff1)\n",
" print('Max absolute difference between deep neural network and analytical: %g'%diff2)\n",
"\n",
" # Plot results\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.plot(t,g_euler)\n",
" plt.plot(t,g_analytical)\n",
" plt.plot(t,g_dnn_ag[0,:])\n",
"\n",
" plt.legend(['euler','analytical','dnn'])\n",
" plt.xlabel('Time t')\n",
" plt.ylabel('g(t)')\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "fa8f0bb4",
"metadata": {
"editable": true
},
"source": [
"## Solving the one dimensional Poisson equation\n",
"\n",
"The Poisson equation for $g(x)$ in one dimension is"
]
},
{
"cell_type": "markdown",
"id": "f765b0ba",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{poisson} \\tag{13}\n",
" -g''(x) = f(x)\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "bd63b92e",
"metadata": {
"editable": true
},
"source": [
"where $f(x)$ is a given function for $x \\in (0,1)$.\n",
"\n",
"The conditions that $g(x)$ is chosen to fulfill, are"
]
},
{
"cell_type": "markdown",
"id": "c0a7face",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{align*}\n",
" g(0) &= 0 \\\\\n",
" g(1) &= 0\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "f71c3cb9",
"metadata": {
"editable": true
},
"source": [
"This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n",
"The results from the networks can then be compared to the analytical solution.\n",
"In addition, it could be interesting to see how a typical method for numerically solving second order ODEs compares to the neural networks.\n",
"\n",
"Here, the function $g(x)$ to solve for follows the equation"
]
},
{
"cell_type": "markdown",
"id": "35aa6a37",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"-g''(x) = f(x),\\qquad x \\in (0,1)\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "f8b35111",
"metadata": {
"editable": true
},
"source": [
"where $f(x)$ is a given function, along with the chosen conditions"
]
},
{
"cell_type": "markdown",
"id": "33813514",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"g(0) = g(1) = 0\n",
"\\end{aligned}\\label{cond} \\tag{14}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "c70aadd4",
"metadata": {
"editable": true
},
"source": [
"In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n",
"\n",
"For this case, a possible trial solution satisfying the conditions could be"
]
},
{
"cell_type": "markdown",
"id": "d5719dee",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "a683041b",
"metadata": {
"editable": true
},
"source": [
"The analytical solution for this problem is"
]
},
{
"cell_type": "markdown",
"id": "672cdaff",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"g(x) = x(1 - x)\\exp(x)\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "66e6bebb",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 457.256\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
" return asarray(a).size\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost: 0.00310113\n",
"The max absolute difference between the solutions is: 0.000464088\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_79_3.png"
}
},
"output_type": "display_data"
}
],
"source": [
"import autograd.numpy as np\n",
"from autograd import grad, elementwise_grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import pyplot as plt\n",
"\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"def deep_neural_network(deep_params, x):\n",
" # N_hidden is the number of hidden layers\n",
" N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
"\n",
" # Assumes input x being an one-dimensional array\n",
" num_values = np.size(x)\n",
" x = x.reshape(-1, num_values)\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
"\n",
" # Due to multiple hidden layers, define a variable referencing to the\n",
" # output of the previous layer:\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = deep_params[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = deep_params[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output\n",
"\n",
"def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
" # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
"\n",
" # Find the number of hidden layers:\n",
" N_hidden = np.size(num_neurons)\n",
"\n",
" ## Set up initial weigths and biases\n",
"\n",
" # Initialize the list of parameters:\n",
" P = [None]*(N_hidden + 1) # + 1 to include the output layer\n",
"\n",
" P[0] = npr.randn(num_neurons[0], 2 )\n",
" for l in range(1,N_hidden):\n",
" P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias\n",
"\n",
" # For the output layer\n",
" P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included\n",
"\n",
" print('Initial cost: %g'%cost_function_deep(P, x))\n",
"\n",
" ## Start finding the optimal weigths using gradient descent\n",
"\n",
" # Find the Python function that represents the gradient of the cost function\n",
" # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer\n",
" cost_function_deep_grad = grad(cost_function_deep,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" # Evaluate the gradient at the current weights and biases in P.\n",
" # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases\n",
" # in the hidden layers and output layers evaluated at x.\n",
" cost_deep_grad = cost_function_deep_grad(P, x)\n",
"\n",
" for l in range(N_hidden+1):\n",
" P[l] = P[l] - lmb * cost_deep_grad[l]\n",
"\n",
" print('Final cost: %g'%cost_function_deep(P, x))\n",
"\n",
" return P\n",
"\n",
"## Set up the cost function specified for this Poisson equation:\n",
"\n",
"# The right side of the ODE\n",
"def f(x):\n",
" return (3*x + x**2)*np.exp(x)\n",
"\n",
"def cost_function_deep(P, x):\n",
"\n",
" # Evaluate the trial function with the current parameters P\n",
" g_t = g_trial_deep(x,P)\n",
"\n",
" # Find the derivative w.r.t x of the trial function\n",
" d2_g_t = elementwise_grad(elementwise_grad(g_trial_deep,0))(x,P)\n",
"\n",
" right_side = f(x)\n",
"\n",
" err_sqr = (-d2_g_t - right_side)**2\n",
" cost_sum = np.sum(err_sqr)\n",
"\n",
" return cost_sum/np.size(err_sqr)\n",
"\n",
"# The trial solution:\n",
"def g_trial_deep(x,P):\n",
" return x*(1-x)*deep_neural_network(P,x)\n",
"\n",
"# The analytic solution;\n",
"def g_analytic(x):\n",
" return x*(1-x)*np.exp(x)\n",
"\n",
"if __name__ == '__main__':\n",
" npr.seed(4155)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" Nx = 10\n",
" x = np.linspace(0,1, Nx)\n",
"\n",
" ## Set up the initial parameters\n",
" num_hidden_neurons = [200,100]\n",
" num_iter = 1000\n",
" lmb = 1e-3\n",
"\n",
" P = solve_ode_deep_neural_network(x, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" g_dnn_ag = g_trial_deep(x,P)\n",
" g_analytical = g_analytic(x)\n",
"\n",
" # Find the maximum absolute difference between the solutons:\n",
" max_diff = np.max(np.abs(g_dnn_ag - g_analytical))\n",
" print(\"The max absolute difference between the solutions is: %g\"%max_diff)\n",
"\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.title('Performance of neural network solving an ODE compared to the analytical solution')\n",
" plt.plot(x, g_analytical)\n",
" plt.plot(x, g_dnn_ag[0,:])\n",
" plt.legend(['analytical','nn'])\n",
" plt.xlabel('x')\n",
" plt.ylabel('g(x)')\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "d425cba5",
"metadata": {
"editable": true
},
"source": [
"### Comparing with a numerical scheme\n",
"\n",
"The Poisson equation is possible to solve using Taylor series to approximate the second derivative.\n",
"\n",
"Using Taylor series, the second derivative can be expressed as\n",
"\n",
"$$\n",
"g''(x) = \\frac{g(x + \\Delta x) - 2g(x) + g(x-\\Delta x)}{\\Delta x^2} + E_{\\Delta x}(x)\n",
"$$\n",
"\n",
"where $\\Delta x$ is a small step size and $E_{\\Delta x}(x)$ being the error term.\n",
"\n",
"Looking away from the error terms gives an approximation to the second derivative:"
]
},
{
"cell_type": "markdown",
"id": "a2efa110",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{approx} \\tag{15}\n",
"g''(x) \\approx \\frac{g(x + \\Delta x) - 2g(x) + g(x-\\Delta x)}{\\Delta x^2}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "5011ee25",
"metadata": {
"editable": true
},
"source": [
"If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes"
]
},
{
"cell_type": "markdown",
"id": "705ee300",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{aligned}\n",
"g''(x_i) &\\approx \\frac{g(x_i + \\Delta x) - 2g(x_i) + g(x_i -\\Delta x)}{\\Delta x^2} \\\\\n",
"&= \\frac{g_{i+1} - 2g_i + g_{i-1}}{\\Delta x^2}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "b390796d",
"metadata": {
"editable": true
},
"source": [
"Since we know from our problem that"
]
},
{
"cell_type": "markdown",
"id": "19c9ece4",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{aligned}\n",
"-g''(x) &= f(x) \\\\\n",
"&= (3x + x^2)\\exp(x)\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "6ade1a7a",
"metadata": {
"editable": true
},
"source": [
"along with the conditions $g(0) = g(1) = 0$,\n",
"the following scheme can be used to find an approximate solution for $g(x)$ numerically:"
]
},
{
"cell_type": "markdown",
"id": "78b16d02",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation}\n",
" \\begin{aligned}\n",
" -\\Big( \\frac{g_{i+1} - 2g_i + g_{i-1}}{\\Delta x^2} \\Big) &= f(x_i) \\\\\n",
" -g_{i+1} + 2g_i - g_{i-1} &= \\Delta x^2 f(x_i)\n",
" \\end{aligned}\n",
"\\end{equation} \\label{odesys} \\tag{16}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "f2bfcca4",
"metadata": {
"editable": true
},
"source": [
"for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n",
"\n",
"The equation can be rewritten into a matrix equation:"
]
},
{
"cell_type": "markdown",
"id": "a6191528",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{aligned}\n",
"\\begin{pmatrix}\n",
"2 & -1 & 0 & \\dots & 0 \\\\\n",
"-1 & 2 & -1 & \\dots & 0 \\\\\n",
"\\vdots & & \\ddots & & \\vdots \\\\\n",
"0 & \\dots & -1 & 2 & -1 \\\\\n",
"0 & \\dots & 0 & -1 & 2\\\\\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"g_1 \\\\\n",
"g_2 \\\\\n",
"\\vdots \\\\\n",
"g_{N_x - 3} \\\\\n",
"g_{N_x - 2}\n",
"\\end{pmatrix}\n",
"&=\n",
"\\Delta x^2\n",
"\\begin{pmatrix}\n",
"f(x_1) \\\\\n",
"f(x_2) \\\\\n",
"\\vdots \\\\\n",
"f(x_{N_x - 3}) \\\\\n",
"f(x_{N_x - 2})\n",
"\\end{pmatrix} \\\\\n",
"\\boldsymbol{A}\\boldsymbol{g} &= \\boldsymbol{f},\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "aefef707",
"metadata": {
"editable": true
},
"source": [
"which makes it possible to solve for the vector $\\boldsymbol{g}$.\n",
"\n",
"We can then compare the result from this numerical scheme with the output from our network using Autograd:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "471664cd",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 457.256\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
" return asarray(a).size\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Final cost: 0.00310113\n",
"The max absolute difference between the analytical solution and DNN Autograd: 0.000464088\n",
"The max absolute difference between the analytical solution and numerical scheme: 0.00266858\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"filenames": {
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_91_4.png"
}
},
"output_type": "display_data"
}
],
"source": [
"import autograd.numpy as np\n",
"from autograd import grad, elementwise_grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import pyplot as plt\n",
"\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"def deep_neural_network(deep_params, x):\n",
" # N_hidden is the number of hidden layers\n",
" N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
"\n",
" # Assumes input x being an one-dimensional array\n",
" num_values = np.size(x)\n",
" x = x.reshape(-1, num_values)\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
"\n",
" # Due to multiple hidden layers, define a variable referencing to the\n",
" # output of the previous layer:\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = deep_params[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = deep_params[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_values)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output\n",
"\n",
"def solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb):\n",
" # num_hidden_neurons is now a list of number of neurons within each hidden layer\n",
"\n",
" # Find the number of hidden layers:\n",
" N_hidden = np.size(num_neurons)\n",
"\n",
" ## Set up initial weigths and biases\n",
"\n",
" # Initialize the list of parameters:\n",
" P = [None]*(N_hidden + 1) # + 1 to include the output layer\n",
"\n",
" P[0] = npr.randn(num_neurons[0], 2 )\n",
" for l in range(1,N_hidden):\n",
" P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias\n",
"\n",
" # For the output layer\n",
" P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included\n",
"\n",
" print('Initial cost: %g'%cost_function_deep(P, x))\n",
"\n",
" ## Start finding the optimal weigths using gradient descent\n",
"\n",
" # Find the Python function that represents the gradient of the cost function\n",
" # w.r.t the 0-th input argument -- that is the weights and biases in the hidden and output layer\n",
" cost_function_deep_grad = grad(cost_function_deep,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" # Evaluate the gradient at the current weights and biases in P.\n",
" # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases\n",
" # in the hidden layers and output layers evaluated at x.\n",
" cost_deep_grad = cost_function_deep_grad(P, x)\n",
"\n",
" for l in range(N_hidden+1):\n",
" P[l] = P[l] - lmb * cost_deep_grad[l]\n",
"\n",
" print('Final cost: %g'%cost_function_deep(P, x))\n",
"\n",
" return P\n",
"\n",
"## Set up the cost function specified for this Poisson equation:\n",
"\n",
"# The right side of the ODE\n",
"def f(x):\n",
" return (3*x + x**2)*np.exp(x)\n",
"\n",
"def cost_function_deep(P, x):\n",
"\n",
" # Evaluate the trial function with the current parameters P\n",
" g_t = g_trial_deep(x,P)\n",
"\n",
" # Find the derivative w.r.t x of the trial function\n",
" d2_g_t = elementwise_grad(elementwise_grad(g_trial_deep,0))(x,P)\n",
"\n",
" right_side = f(x)\n",
"\n",
" err_sqr = (-d2_g_t - right_side)**2\n",
" cost_sum = np.sum(err_sqr)\n",
"\n",
" return cost_sum/np.size(err_sqr)\n",
"\n",
"# The trial solution:\n",
"def g_trial_deep(x,P):\n",
" return x*(1-x)*deep_neural_network(P,x)\n",
"\n",
"# The analytic solution;\n",
"def g_analytic(x):\n",
" return x*(1-x)*np.exp(x)\n",
"\n",
"if __name__ == '__main__':\n",
" npr.seed(4155)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" Nx = 10\n",
" x = np.linspace(0,1, Nx)\n",
"\n",
" ## Set up the initial parameters\n",
" num_hidden_neurons = [200,100]\n",
" num_iter = 1000\n",
" lmb = 1e-3\n",
"\n",
" P = solve_ode_deep_neural_network(x, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" g_dnn_ag = g_trial_deep(x,P)\n",
" g_analytical = g_analytic(x)\n",
"\n",
" # Find the maximum absolute difference between the solutons:\n",
"\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.title('Performance of neural network solving an ODE compared to the analytical solution')\n",
" plt.plot(x, g_analytical)\n",
" plt.plot(x, g_dnn_ag[0,:])\n",
" plt.legend(['analytical','nn'])\n",
" plt.xlabel('x')\n",
" plt.ylabel('g(x)')\n",
"\n",
" ## Perform the computation using the numerical scheme\n",
"\n",
" dx = 1/(Nx - 1)\n",
"\n",
" # Set up the matrix A\n",
" A = np.zeros((Nx-2,Nx-2))\n",
"\n",
" A[0,0] = 2\n",
" A[0,1] = -1\n",
"\n",
" for i in range(1,Nx-3):\n",
" A[i,i-1] = -1\n",
" A[i,i] = 2\n",
" A[i,i+1] = -1\n",
"\n",
" A[Nx - 3, Nx - 4] = -1\n",
" A[Nx - 3, Nx - 3] = 2\n",
"\n",
" # Set up the vector f\n",
" f_vec = dx**2 * f(x[1:-1])\n",
"\n",
" # Solve the equation\n",
" g_res = np.linalg.solve(A,f_vec)\n",
"\n",
" g_vec = np.zeros(Nx)\n",
" g_vec[1:-1] = g_res\n",
"\n",
" # Print the differences between each method\n",
" max_diff1 = np.max(np.abs(g_dnn_ag - g_analytical))\n",
" max_diff2 = np.max(np.abs(g_vec - g_analytical))\n",
" print(\"The max absolute difference between the analytical solution and DNN Autograd: %g\"%max_diff1)\n",
" print(\"The max absolute difference between the analytical solution and numerical scheme: %g\"%max_diff2)\n",
"\n",
" # Plot the results\n",
" plt.figure(figsize=(10,10))\n",
"\n",
" plt.plot(x,g_vec)\n",
" plt.plot(x,g_analytical)\n",
" plt.plot(x,g_dnn_ag[0,:])\n",
"\n",
" plt.legend(['numerical scheme','analytical','dnn'])\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "6f02e86d",
"metadata": {
"editable": true
},
"source": [
"## Partial Differential Equations\n",
"\n",
"A partial differential equation (PDE) has a solution here the function\n",
"is defined by multiple variables. The equation may involve all kinds\n",
"of combinations of which variables the function is differentiated with\n",
"respect to.\n",
"\n",
"In general, a partial differential equation for a function $g(x_1,\\dots,x_N)$ with $N$ variables may be expressed as"
]
},
{
"cell_type": "markdown",
"id": "ad5c63e8",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{PDE} \\tag{17}\n",
" f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) = 0\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "c7b98797",
"metadata": {
"editable": true
},
"source": [
"where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given."
]
},
{
"cell_type": "markdown",
"id": "52f9394e",
"metadata": {
"editable": true
},
"source": [
"### Type of problem\n",
"\n",
"The problem our network must solve for, is similar to the ODE case.\n",
"We must have a trial solution $g_t$ at hand.\n",
"\n",
"For instance, the trial solution could be expressed as"
]
},
{
"cell_type": "markdown",
"id": "4d489854",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{align*}\n",
" g_t(x_1,\\dots,x_N) = h_1(x_1,\\dots,x_N) + h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "82311538",
"metadata": {
"editable": true
},
"source": [
"where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n",
"The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n",
"\n",
"The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions."
]
},
{
"cell_type": "markdown",
"id": "9d134db4",
"metadata": {
"editable": true
},
"source": [
"### Network requirements\n",
"\n",
"The network tries then the minimize the cost function following the\n",
"same ideas as described for the ODE case, but now with more than one\n",
"variables to consider. The concept still remains the same; find a set\n",
"of parameters $P$ such that the expression $f$ in ([17](#PDE)) is as\n",
"close to zero as possible.\n",
"\n",
"As for the ODE case, the cost function is the mean squared error that\n",
"the network must try to minimize. The cost function for the network to\n",
"minimize is"
]
},
{
"cell_type": "markdown",
"id": "5a463498",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"C\\left(x_1, \\dots, x_N, P\\right) = \\left( f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "c40d8997",
"metadata": {
"editable": true
},
"source": [
"If we let $\\boldsymbol{x} = \\big( x_1, \\dots, x_N \\big)$ be an array containing the values for $x_1, \\dots, x_N$ respectively, the cost function can be reformulated into the following:"
]
},
{
"cell_type": "markdown",
"id": "cc033de6",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ae18b4f4",
"metadata": {
"editable": true
},
"source": [
"If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into"
]
},
{
"cell_type": "markdown",
"id": "44ca21bd",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "fe94451e",
"metadata": {
"editable": true
},
"source": [
"## Example: The diffusion equation\n",
"\n",
"In one spatial dimension, the equation reads"
]
},
{
"cell_type": "markdown",
"id": "30a42273",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "fd4077e7",
"metadata": {
"editable": true
},
"source": [
"where a possible choice of conditions are"
]
},
{
"cell_type": "markdown",
"id": "dbbf2e4b",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{align*}\n",
"g(0,t) &= 0 ,\\qquad t \\geq 0 \\\\\n",
"g(1,t) &= 0, \\qquad t \\geq 0 \\\\\n",
"g(x,0) &= u(x),\\qquad x\\in [0,1]\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "83653db9",
"metadata": {
"editable": true
},
"source": [
"with $u(x)$ being some given function.\n",
"\n",
"For this case, we want to find $g(x,t)$ such that"
]
},
{
"cell_type": "markdown",
"id": "d2c2ef4f",
"metadata": {
"editable": true
},
"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation}\n",
" \\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
"\\end{equation} \\label{diffonedim} \\tag{18}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "8fb27bdb",
"metadata": {
"editable": true
},
"source": [
"and"
]
},
{
"cell_type": "markdown",
"id": "dc9297ab",
"metadata": {
"editable": true
},
"source": [
"$$\n",
"\\begin{align*}\n",
"g(0,t) &= 0 ,\\qquad t \\geq 0 \\\\\n",
"g(1,t) &= 0, \\qquad t \\geq 0 \\\\\n",
"g(x,0) &= u(x),\\qquad x\\in [0,1]\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ab90784f",
"metadata": {
"editable": true
},
"source": [
"with $u(x) = \\sin(\\pi x)$.\n",
"\n",
"First, let us set up the deep neural network.\n",
"The deep neural network will follow the same structure as discussed in the examples solving the ODEs.\n",
"First, we will look into how Autograd could be used in a network tailored to solve for bivariate functions.\n",
"\n",
"The only change to do here, is to extend our network such that\n",
"functions of multiple parameters are correctly handled. In this case\n",
"we have two variables in our function to solve for, that is time $t$\n",
"and position $x$. The variables will be represented by a\n",
"one-dimensional array in the program. The program will evaluate the\n",
"network at each possible pair $(x,t)$, given an array for the desired\n",
"$x$-values and $t$-values to approximate the solution at."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b07e858c",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [],
"source": [
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"def deep_neural_network(deep_params, x):\n",
" # x is now a point and a 1D numpy array; make it a column vector\n",
" num_coordinates = np.size(x,0)\n",
" x = x.reshape(num_coordinates,-1)\n",
"\n",
" num_points = np.size(x,1)\n",
"\n",
" # N_hidden is the number of hidden layers\n",
" N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = deep_params[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_points)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = deep_params[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_points)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output[0][0]"
]
},
{
"cell_type": "markdown",
"id": "9a167ec1",
"metadata": {
"editable": true
},
"source": [
"The cost function must then iterate through the given arrays\n",
"containing values for $x$ and $t$, defines a point $(x,t)$ the deep\n",
"neural network and the trial solution is evaluated at, and then finds\n",
"the Jacobian of the trial solution.\n",
"\n",
"A possible trial solution for this PDE is\n",
"\n",
"$$\n",
"g_t(x,t) = h_1(x,t) + x(1-x)tN(x,t,P)\n",
"$$\n",
"\n",
"with $A(x,t)$ being a function ensuring that $g_t(x,t)$ satisfies our given conditions, and $N(x,t,P)$ being the output from the deep neural network using weights and biases for each layer from $P$.\n",
"\n",
"To fulfill the conditions, $A(x,t)$ could be:\n",
"\n",
"$$\n",
"h_1(x,t) = (1-t)\\Big(u(x) - \\big((1-x)u(0) + x u(1)\\big)\\Big) = (1-t)u(x) = (1-t)\\sin(\\pi x)\n",
"$$\n",
"since $(0) = u(1) = 0$ and $u(x) = \\sin(\\pi x)$.\n",
"\n",
"The Jacobian is used because the program must find the derivative of\n",
"the trial solution with respect to $x$ and $t$.\n",
"\n",
"This gives the necessity of computing the Jacobian matrix, as we want\n",
"to evaluate the gradient with respect to $x$ and $t$ (note that the\n",
"Jacobian of a scalar-valued multivariate function is simply its\n",
"gradient).\n",
"\n",
"In Autograd, the differentiation is by default done with respect to\n",
"the first input argument of your Python function. Since the points is\n",
"an array representing $x$ and $t$, the Jacobian is calculated using\n",
"the values of $x$ and $t$.\n",
"\n",
"To find the second derivative with respect to $x$ and $t$, the\n",
"Jacobian can be found for the second time. The result is a Hessian\n",
"matrix, which is the matrix containing all the possible second order\n",
"mixed derivatives of $g(x,t)$."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "921e5969",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [],
"source": [
"# Set up the trial function:\n",
"def u(x):\n",
" return np.sin(np.pi*x)\n",
"\n",
"def g_trial(point,P):\n",
" x,t = point\n",
" return (1-t)*u(x) + x*(1-x)*t*deep_neural_network(P,point)\n",
"\n",
"# The right side of the ODE:\n",
"def f(point):\n",
" return 0.\n",
"\n",
"# The cost function:\n",
"def cost_function(P, x, t):\n",
" cost_sum = 0\n",
"\n",
" g_t_jacobian_func = jacobian(g_trial)\n",
" g_t_hessian_func = hessian(g_trial)\n",
"\n",
" for x_ in x:\n",
" for t_ in t:\n",
" point = np.array([x_,t_])\n",
"\n",
" g_t = g_trial(point,P)\n",
" g_t_jacobian = g_t_jacobian_func(point,P)\n",
" g_t_hessian = g_t_hessian_func(point,P)\n",
"\n",
" g_t_dt = g_t_jacobian[1]\n",
" g_t_d2x = g_t_hessian[0][0]\n",
"\n",
" func = f(point)\n",
"\n",
" err_sqr = ( (g_t_dt - g_t_d2x) - func)**2\n",
" cost_sum += err_sqr\n",
"\n",
" return cost_sum"
]
},
{
"cell_type": "markdown",
"id": "0bc00b69",
"metadata": {
"editable": true
},
"source": [
"### Setting up the network using Autograd; The full program\n",
"\n",
"Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.\n",
"\n",
"The analytical solution of our problem is\n",
"\n",
"$$\n",
"g(x,t) = \\exp(-\\pi^2 t)\\sin(\\pi x)\n",
"$$\n",
"\n",
"A possible way to implement a neural network solving the PDE, is given below.\n",
"Be aware, though, that it is fairly slow for the parameters used.\n",
"A better result is possible, but requires more iterations, and thus longer time to complete.\n",
"\n",
"Indeed, the program below is not optimal in its implementation, but rather serves as an example on how to implement and use a neural network to solve a PDE.\n",
"Using TensorFlow results in a much better execution time. Try it!"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "20734418",
"metadata": {
"collapsed": false,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
" return asarray(a).size\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cost: 41.05505310046363\n"
]
},
{
"ename": "KeyboardInterrupt",
"evalue": "",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
"Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 140\u001b[0m num_iter \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m250\u001b[39m\n\u001b[1;32m 141\u001b[0m lmb \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.01\u001b[39m\n\u001b[0;32m--> 143\u001b[0m P \u001b[38;5;241m=\u001b[39m \u001b[43msolve_pde_deep_neural_network\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_hidden_neurons\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_iter\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlmb\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 145\u001b[0m \u001b[38;5;66;03m## Store the results\u001b[39;00m\n\u001b[1;32m 146\u001b[0m g_dnn_ag \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros((Nx, Nt))\n",
"Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36msolve_pde_deep_neural_network\u001b[0;34m(x, t, num_neurons, num_iter, lmb)\u001b[0m\n\u001b[1;32m 118\u001b[0m \u001b[38;5;66;03m# Let the update be done num_iter times\u001b[39;00m\n\u001b[1;32m 119\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(num_iter):\n\u001b[0;32m--> 120\u001b[0m cost_grad \u001b[38;5;241m=\u001b[39m \u001b[43mcost_function_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mP\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 122\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m l \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(N_hidden\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[1;32m 123\u001b[0m P[l] \u001b[38;5;241m=\u001b[39m P[l] \u001b[38;5;241m-\u001b[39m lmb \u001b[38;5;241m*\u001b[39m cost_grad[l]\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad\u001b[39m(fun, x):\n\u001b[1;32m 20\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 21\u001b[0m \u001b[38;5;124;03m Returns a function which computes the gradient of `fun` with respect to\u001b[39;00m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;124;03m positional argument number `argnum`. The returned function takes the same\u001b[39;00m\n\u001b[1;32m 23\u001b[0m \u001b[38;5;124;03m arguments as `fun`, but returns the gradient instead. The function `fun`\u001b[39;00m\n\u001b[1;32m 24\u001b[0m \u001b[38;5;124;03m should be scalar-valued. The gradient has the same type as the argument.\"\"\"\u001b[39;00m\n\u001b[0;32m---> 25\u001b[0m vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 26\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m 27\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 28\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m 9\u001b[0m start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m end_value, end_node \u001b[38;5;241m=\u001b[39m \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m 9\u001b[0m start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f..unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 14\u001b[0m subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
"Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36mcost_function\u001b[0;34m(P, x, t)\u001b[0m\n\u001b[1;32m 78\u001b[0m g_t \u001b[38;5;241m=\u001b[39m g_trial(point,P)\n\u001b[1;32m 79\u001b[0m g_t_jacobian \u001b[38;5;241m=\u001b[39m g_t_jacobian_func(point,P)\n\u001b[0;32m---> 80\u001b[0m g_t_hessian \u001b[38;5;241m=\u001b[39m \u001b[43mg_t_hessian_func\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpoint\u001b[49m\u001b[43m,\u001b[49m\u001b[43mP\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 82\u001b[0m g_t_dt \u001b[38;5;241m=\u001b[39m g_t_jacobian[\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m 83\u001b[0m g_t_d2x \u001b[38;5;241m=\u001b[39m g_t_hessian[\u001b[38;5;241m0\u001b[39m][\u001b[38;5;241m0\u001b[39m]\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:78\u001b[0m, in \u001b[0;36mhessian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 75\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 76\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhessian\u001b[39m(fun, x):\n\u001b[1;32m 77\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mReturns a function that computes the exact Hessian.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m---> 78\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary..nary_operator..nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:61\u001b[0m, in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 59\u001b[0m jacobian_shape \u001b[38;5;241m=\u001b[39m ans_vspace\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m+\u001b[39m vspace(x)\u001b[38;5;241m.\u001b[39mshape\n\u001b[1;32m 60\u001b[0m grads \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(vjp, ans_vspace\u001b[38;5;241m.\u001b[39mstandard_basis())\n\u001b[0;32m---> 61\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mreshape(\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstack\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgrads\u001b[49m\u001b[43m)\u001b[49m, jacobian_shape)\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36mstack\u001b[0;34m(arrays, axis)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m 84\u001b[0m \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m 89\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m 90\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m 84\u001b[0m \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m 89\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m 90\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14\u001b[0m, in \u001b[0;36mmake_vjp..vjp\u001b[0;34m(g)\u001b[0m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackward_pass\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend_node\u001b[49m\u001b[43m)\u001b[49m\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m toposort(end_node):\n\u001b[1;32m 20\u001b[0m outgrad \u001b[38;5;241m=\u001b[39m outgrads\u001b[38;5;241m.\u001b[39mpop(node)\n\u001b[0;32m---> 21\u001b[0m ingrads \u001b[38;5;241m=\u001b[39m \u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrad\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[1;32m 23\u001b[0m outgrads[parent] \u001b[38;5;241m=\u001b[39m add_outgrads(outgrads\u001b[38;5;241m.\u001b[39mget(parent), ingrad)\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67\u001b[0m, in \u001b[0;36mdefvjp..vjp_argnums..\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m 65\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m 66\u001b[0m vjp \u001b[38;5;241m=\u001b[39m vjpfun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 67\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m,)\n\u001b[1;32m 68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m 69\u001b[0m argnum_0, argnum_1 \u001b[38;5;241m=\u001b[39m argnums\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:82\u001b[0m, in \u001b[0;36m\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 80\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mlog10, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x : \u001b[38;5;28;01mlambda\u001b[39;00m g: g \u001b[38;5;241m/\u001b[39m x \u001b[38;5;241m/\u001b[39m anp\u001b[38;5;241m.\u001b[39mlog(\u001b[38;5;241m10\u001b[39m))\n\u001b[1;32m 81\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mlog1p, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x : \u001b[38;5;28;01mlambda\u001b[39;00m g: g \u001b[38;5;241m/\u001b[39m (x \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1\u001b[39m))\n\u001b[0;32m---> 82\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39msin, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x : \u001b[38;5;28;01mlambda\u001b[39;00m g: g \u001b[38;5;241m*\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcos\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m 83\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mcos, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x : \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[38;5;241m-\u001b[39m g \u001b[38;5;241m*\u001b[39m anp\u001b[38;5;241m.\u001b[39msin(x))\n\u001b[1;32m 84\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mtan, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x : \u001b[38;5;28;01mlambda\u001b[39;00m g: g \u001b[38;5;241m/\u001b[39m anp\u001b[38;5;241m.\u001b[39mcos(x) \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m)\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:37\u001b[0m, in \u001b[0;36mprimitive..f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 35\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(f_raw)\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf_wrapped\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m---> 37\u001b[0m boxed_args, trace, node_constructor \u001b[38;5;241m=\u001b[39m \u001b[43mfind_top_boxed_args\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 38\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m boxed_args:\n\u001b[1;32m 39\u001b[0m argvals \u001b[38;5;241m=\u001b[39m subvals(args, [(argnum, box\u001b[38;5;241m.\u001b[39m_value) \u001b[38;5;28;01mfor\u001b[39;00m argnum, box \u001b[38;5;129;01min\u001b[39;00m boxed_args])\n",
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:70\u001b[0m, in \u001b[0;36mfind_top_boxed_args\u001b[0;34m(args)\u001b[0m\n\u001b[1;32m 68\u001b[0m top_node_type \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m 69\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m argnum, arg \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(args):\n\u001b[0;32m---> 70\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[43misbox\u001b[49m\u001b[43m(\u001b[49m\u001b[43marg\u001b[49m\u001b[43m)\u001b[49m:\n\u001b[1;32m 71\u001b[0m trace \u001b[38;5;241m=\u001b[39m arg\u001b[38;5;241m.\u001b[39m_trace\n\u001b[1;32m 72\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m trace \u001b[38;5;241m>\u001b[39m top_trace:\n",
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
]
}
],
"source": [
"import autograd.numpy as np\n",
"from autograd import jacobian,hessian,grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import cm\n",
"from matplotlib import pyplot as plt\n",
"from mpl_toolkits.mplot3d import axes3d\n",
"\n",
"## Set up the network\n",
"\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"def deep_neural_network(deep_params, x):\n",
" # x is now a point and a 1D numpy array; make it a column vector\n",
" num_coordinates = np.size(x,0)\n",
" x = x.reshape(num_coordinates,-1)\n",
"\n",
" num_points = np.size(x,1)\n",
"\n",
" # N_hidden is the number of hidden layers\n",
" N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = deep_params[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_points)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = deep_params[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_points)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output[0][0]\n",
"\n",
"## Define the trial solution and cost function\n",
"def u(x):\n",
" return np.sin(np.pi*x)\n",
"\n",
"def g_trial(point,P):\n",
" x,t = point\n",
" return (1-t)*u(x) + x*(1-x)*t*deep_neural_network(P,point)\n",
"\n",
"# The right side of the ODE:\n",
"def f(point):\n",
" return 0.\n",
"\n",
"# The cost function:\n",
"def cost_function(P, x, t):\n",
" cost_sum = 0\n",
"\n",
" g_t_jacobian_func = jacobian(g_trial)\n",
" g_t_hessian_func = hessian(g_trial)\n",
"\n",
" for x_ in x:\n",
" for t_ in t:\n",
" point = np.array([x_,t_])\n",
"\n",
" g_t = g_trial(point,P)\n",
" g_t_jacobian = g_t_jacobian_func(point,P)\n",
" g_t_hessian = g_t_hessian_func(point,P)\n",
"\n",
" g_t_dt = g_t_jacobian[1]\n",
" g_t_d2x = g_t_hessian[0][0]\n",
"\n",
" func = f(point)\n",
"\n",
" err_sqr = ( (g_t_dt - g_t_d2x) - func)**2\n",
" cost_sum += err_sqr\n",
"\n",
" return cost_sum /( np.size(x)*np.size(t) )\n",
"\n",
"## For comparison, define the analytical solution\n",
"def g_analytic(point):\n",
" x,t = point\n",
" return np.exp(-np.pi**2*t)*np.sin(np.pi*x)\n",
"\n",
"## Set up a function for training the network to solve for the equation\n",
"def solve_pde_deep_neural_network(x,t, num_neurons, num_iter, lmb):\n",
" ## Set up initial weigths and biases\n",
" N_hidden = np.size(num_neurons)\n",
"\n",
" ## Set up initial weigths and biases\n",
"\n",
" # Initialize the list of parameters:\n",
" P = [None]*(N_hidden + 1) # + 1 to include the output layer\n",
"\n",
" P[0] = npr.randn(num_neurons[0], 2 + 1 ) # 2 since we have two points, +1 to include bias\n",
" for l in range(1,N_hidden):\n",
" P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias\n",
"\n",
" # For the output layer\n",
" P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included\n",
"\n",
" print('Initial cost: ',cost_function(P, x, t))\n",
"\n",
" cost_function_grad = grad(cost_function,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" cost_grad = cost_function_grad(P, x , t)\n",
"\n",
" for l in range(N_hidden+1):\n",
" P[l] = P[l] - lmb * cost_grad[l]\n",
"\n",
" print('Final cost: ',cost_function(P, x, t))\n",
"\n",
" return P\n",
"\n",
"if __name__ == '__main__':\n",
" ### Use the neural network:\n",
" npr.seed(15)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" Nx = 10; Nt = 10\n",
" x = np.linspace(0, 1, Nx)\n",
" t = np.linspace(0,1,Nt)\n",
"\n",
" ## Set up the parameters for the network\n",
" num_hidden_neurons = [100, 25]\n",
" num_iter = 250\n",
" lmb = 0.01\n",
"\n",
" P = solve_pde_deep_neural_network(x,t, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" ## Store the results\n",
" g_dnn_ag = np.zeros((Nx, Nt))\n",
" G_analytical = np.zeros((Nx, Nt))\n",
" for i,x_ in enumerate(x):\n",
" for j, t_ in enumerate(t):\n",
" point = np.array([x_, t_])\n",
" g_dnn_ag[i,j] = g_trial(point,P)\n",
"\n",
" G_analytical[i,j] = g_analytic(point)\n",
"\n",
" # Find the map difference between the analytical and the computed solution\n",
" diff_ag = np.abs(g_dnn_ag - G_analytical)\n",
" print('Max absolute difference between the analytical solution and the network: %g'%np.max(diff_ag))\n",
"\n",
" ## Plot the solutions in two dimensions, that being in position and time\n",
"\n",
" T,X = np.meshgrid(t,x)\n",
"\n",
" fig = plt.figure(figsize=(10,10))\n",
" ax = fig.gca(projection='3d')\n",
" ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
" s = ax.plot_surface(T,X,g_dnn_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
" ax.set_xlabel('Time $t$')\n",
" ax.set_ylabel('Position $x$');\n",
"\n",
"\n",
" fig = plt.figure(figsize=(10,10))\n",
" ax = fig.gca(projection='3d')\n",
" ax.set_title('Analytical solution')\n",
" s = ax.plot_surface(T,X,G_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
" ax.set_xlabel('Time $t$')\n",
" ax.set_ylabel('Position $x$');\n",
"\n",
" fig = plt.figure(figsize=(10,10))\n",
" ax = fig.gca(projection='3d')\n",
" ax.set_title('Difference')\n",
" s = ax.plot_surface(T,X,diff_ag,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
" ax.set_xlabel('Time $t$')\n",
" ax.set_ylabel('Position $x$');\n",
"\n",
" ## Take some slices of the 3D plots just to see the solutions at particular times\n",
" indx1 = 0\n",
" indx2 = int(Nt/2)\n",
" indx3 = Nt-1\n",
"\n",
" t1 = t[indx1]\n",
" t2 = t[indx2]\n",
" t3 = t[indx3]\n",
"\n",
" # Slice the results from the DNN\n",
" res1 = g_dnn_ag[:,indx1]\n",
" res2 = g_dnn_ag[:,indx2]\n",
" res3 = g_dnn_ag[:,indx3]\n",
"\n",
" # Slice the analytical results\n",
" res_analytical1 = G_analytical[:,indx1]\n",
" res_analytical2 = G_analytical[:,indx2]\n",
" res_analytical3 = G_analytical[:,indx3]\n",
"\n",
" # Plot the slices\n",
" plt.figure(figsize=(10,10))\n",
" plt.title(\"Computed solutions at time = %g\"%t1)\n",
" plt.plot(x, res1)\n",
" plt.plot(x,res_analytical1)\n",
" plt.legend(['dnn','analytical'])\n",
"\n",
" plt.figure(figsize=(10,10))\n",
" plt.title(\"Computed solutions at time = %g\"%t2)\n",
" plt.plot(x, res2)\n",
" plt.plot(x,res_analytical2)\n",
" plt.legend(['dnn','analytical'])\n",
"\n",
" plt.figure(figsize=(10,10))\n",
" plt.title(\"Computed solutions at time = %g\"%t3)\n",
" plt.plot(x, res3)\n",
" plt.plot(x,res_analytical3)\n",
" plt.legend(['dnn','analytical'])\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "143f1c80",
"metadata": {
"editable": true
},
"source": [
"## Solving the wave equation with Neural Networks\n",
"\n",
"The wave equation is"
]
},
{
"cell_type": "markdown",
"id": "190bd4f2",
"metadata": {
"editable": true
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"source": [
"$$\n",
"\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "9719cfc5",
"metadata": {
"editable": true
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"source": [
"with $c$ being the specified wave speed.\n",
"\n",
"Here, the chosen conditions are"
]
},
{
"cell_type": "markdown",
"id": "f69ec7fd",
"metadata": {
"editable": true
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"source": [
"$$\n",
"\\begin{align*}\n",
"\tg(0,t) &= 0 \\\\\n",
"\tg(1,t) &= 0 \\\\\n",
"\tg(x,0) &= u(x) \\\\\n",
"\t\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0} &= v(x)\n",
"\\end{align*}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "6ce8c5a8",
"metadata": {
"editable": true
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"source": [
"where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions.\n",
"\n",
"The wave equation to solve for, is"
]
},
{
"cell_type": "markdown",
"id": "4be700d7",
"metadata": {
"editable": true
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{equation} \\label{wave} \\tag{19}\n",
"\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2 \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "993f93ba",
"metadata": {
"editable": true
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"source": [
"where $c$ is the given wave speed.\n",
"The chosen conditions for this equation are"
]
},
{
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"id": "2cb2a80f",
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"source": [
"\n",
"\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"g(0,t) &= 0, &t \\geq 0 \\\\\n",
"g(1,t) &= 0, &t \\geq 0 \\\\\n",
"g(x,0) &= u(x), &x\\in[0,1] \\\\\n",
"\\frac{\\partial g(x,t)}{\\partial t}\\Big |_{t = 0} &= v(x), &x \\in [0,1]\n",
"\\end{aligned} \\label{condwave} \\tag{20}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "3f1dcfd4",
"metadata": {
"editable": true
},
"source": [
"In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$.\n",
"\n",
"Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n",
"The only things we have to change, is the trial solution such that it satisfies the conditions from ([20](#condwave)) and the cost function.\n",
"\n",
"The trial solution becomes slightly different since we have other conditions than in the example of solving the diffusion equation. Here, a possible trial solution $g_t(x,t)$ is\n",
"\n",
"$$\n",
"g_t(x,t) = h_1(x,t) + x(1-x)t^2N(x,t,P)\n",
"$$\n",
"\n",
"where\n",
"\n",
"$$\n",
"h_1(x,t) = (1-t^2)u(x) + tv(x)\n",
"$$\n",
"\n",
"Note that this trial solution satisfies the conditions only if $u(0) = v(0) = u(1) = v(1) = 0$, which is the case in this example.\n",
"\n",
"The analytical solution for our specific problem, is\n",
"\n",
"$$\n",
"g(x,t) = \\sin(\\pi x)\\cos(\\pi t) - \\sin(\\pi x)\\sin(\\pi t)\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "230a9aef",
"metadata": {
"collapsed": false,
"editable": true
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"outputs": [],
"source": [
"import autograd.numpy as np\n",
"from autograd import hessian,grad\n",
"import autograd.numpy.random as npr\n",
"from matplotlib import cm\n",
"from matplotlib import pyplot as plt\n",
"from mpl_toolkits.mplot3d import axes3d\n",
"\n",
"## Set up the trial function:\n",
"def u(x):\n",
" return np.sin(np.pi*x)\n",
"\n",
"def v(x):\n",
" return -np.pi*np.sin(np.pi*x)\n",
"\n",
"def h1(point):\n",
" x,t = point\n",
" return (1 - t**2)*u(x) + t*v(x)\n",
"\n",
"def g_trial(point,P):\n",
" x,t = point\n",
" return h1(point) + x*(1-x)*t**2*deep_neural_network(P,point)\n",
"\n",
"## Define the cost function\n",
"def cost_function(P, x, t):\n",
" cost_sum = 0\n",
"\n",
" g_t_hessian_func = hessian(g_trial)\n",
"\n",
" for x_ in x:\n",
" for t_ in t:\n",
" point = np.array([x_,t_])\n",
"\n",
" g_t_hessian = g_t_hessian_func(point,P)\n",
"\n",
" g_t_d2x = g_t_hessian[0][0]\n",
" g_t_d2t = g_t_hessian[1][1]\n",
"\n",
" err_sqr = ( (g_t_d2t - g_t_d2x) )**2\n",
" cost_sum += err_sqr\n",
"\n",
" return cost_sum / (np.size(t) * np.size(x))\n",
"\n",
"## The neural network\n",
"def sigmoid(z):\n",
" return 1/(1 + np.exp(-z))\n",
"\n",
"def deep_neural_network(deep_params, x):\n",
" # x is now a point and a 1D numpy array; make it a column vector\n",
" num_coordinates = np.size(x,0)\n",
" x = x.reshape(num_coordinates,-1)\n",
"\n",
" num_points = np.size(x,1)\n",
"\n",
" # N_hidden is the number of hidden layers\n",
" N_hidden = np.size(deep_params) - 1 # -1 since params consist of parameters to all the hidden layers AND the output layer\n",
"\n",
" # Assume that the input layer does nothing to the input x\n",
" x_input = x\n",
" x_prev = x_input\n",
"\n",
" ## Hidden layers:\n",
"\n",
" for l in range(N_hidden):\n",
" # From the list of parameters P; find the correct weigths and bias for this layer\n",
" w_hidden = deep_params[l]\n",
"\n",
" # Add a row of ones to include bias\n",
" x_prev = np.concatenate((np.ones((1,num_points)), x_prev ), axis = 0)\n",
"\n",
" z_hidden = np.matmul(w_hidden, x_prev)\n",
" x_hidden = sigmoid(z_hidden)\n",
"\n",
" # Update x_prev such that next layer can use the output from this layer\n",
" x_prev = x_hidden\n",
"\n",
" ## Output layer:\n",
"\n",
" # Get the weights and bias for this layer\n",
" w_output = deep_params[-1]\n",
"\n",
" # Include bias:\n",
" x_prev = np.concatenate((np.ones((1,num_points)), x_prev), axis = 0)\n",
"\n",
" z_output = np.matmul(w_output, x_prev)\n",
" x_output = z_output\n",
"\n",
" return x_output[0][0]\n",
"\n",
"## The analytical solution\n",
"def g_analytic(point):\n",
" x,t = point\n",
" return np.sin(np.pi*x)*np.cos(np.pi*t) - np.sin(np.pi*x)*np.sin(np.pi*t)\n",
"\n",
"def solve_pde_deep_neural_network(x,t, num_neurons, num_iter, lmb):\n",
" ## Set up initial weigths and biases\n",
" N_hidden = np.size(num_neurons)\n",
"\n",
" ## Set up initial weigths and biases\n",
"\n",
" # Initialize the list of parameters:\n",
" P = [None]*(N_hidden + 1) # + 1 to include the output layer\n",
"\n",
" P[0] = npr.randn(num_neurons[0], 2 + 1 ) # 2 since we have two points, +1 to include bias\n",
" for l in range(1,N_hidden):\n",
" P[l] = npr.randn(num_neurons[l], num_neurons[l-1] + 1) # +1 to include bias\n",
"\n",
" # For the output layer\n",
" P[-1] = npr.randn(1, num_neurons[-1] + 1 ) # +1 since bias is included\n",
"\n",
" print('Initial cost: ',cost_function(P, x, t))\n",
"\n",
" cost_function_grad = grad(cost_function,0)\n",
"\n",
" # Let the update be done num_iter times\n",
" for i in range(num_iter):\n",
" cost_grad = cost_function_grad(P, x , t)\n",
"\n",
" for l in range(N_hidden+1):\n",
" P[l] = P[l] - lmb * cost_grad[l]\n",
"\n",
"\n",
" print('Final cost: ',cost_function(P, x, t))\n",
"\n",
" return P\n",
"\n",
"if __name__ == '__main__':\n",
" ### Use the neural network:\n",
" npr.seed(15)\n",
"\n",
" ## Decide the vales of arguments to the function to solve\n",
" Nx = 10; Nt = 10\n",
" x = np.linspace(0, 1, Nx)\n",
" t = np.linspace(0,1,Nt)\n",
"\n",
" ## Set up the parameters for the network\n",
" num_hidden_neurons = [50,20]\n",
" num_iter = 1000\n",
" lmb = 0.01\n",
"\n",
" P = solve_pde_deep_neural_network(x,t, num_hidden_neurons, num_iter, lmb)\n",
"\n",
" ## Store the results\n",
" res = np.zeros((Nx, Nt))\n",
" res_analytical = np.zeros((Nx, Nt))\n",
" for i,x_ in enumerate(x):\n",
" for j, t_ in enumerate(t):\n",
" point = np.array([x_, t_])\n",
" res[i,j] = g_trial(point,P)\n",
"\n",
" res_analytical[i,j] = g_analytic(point)\n",
"\n",
" diff = np.abs(res - res_analytical)\n",
" print(\"Max difference between analytical and solution from nn: %g\"%np.max(diff))\n",
"\n",
" ## Plot the solutions in two dimensions, that being in position and time\n",
"\n",
" T,X = np.meshgrid(t,x)\n",
"\n",
" fig = plt.figure(figsize=(10,10))\n",
" ax = fig.gca(projection='3d')\n",
" ax.set_title('Solution from the deep neural network w/ %d layer'%len(num_hidden_neurons))\n",
" s = ax.plot_surface(T,X,res,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
" ax.set_xlabel('Time $t$')\n",
" ax.set_ylabel('Position $x$');\n",
"\n",
"\n",
" fig = plt.figure(figsize=(10,10))\n",
" ax = fig.gca(projection='3d')\n",
" ax.set_title('Analytical solution')\n",
" s = ax.plot_surface(T,X,res_analytical,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
" ax.set_xlabel('Time $t$')\n",
" ax.set_ylabel('Position $x$');\n",
"\n",
"\n",
" fig = plt.figure(figsize=(10,10))\n",
" ax = fig.gca(projection='3d')\n",
" ax.set_title('Difference')\n",
" s = ax.plot_surface(T,X,diff,linewidth=0,antialiased=False,cmap=cm.viridis)\n",
" ax.set_xlabel('Time $t$')\n",
" ax.set_ylabel('Position $x$');\n",
"\n",
" ## Take some slices of the 3D plots just to see the solutions at particular times\n",
" indx1 = 0\n",
" indx2 = int(Nt/2)\n",
" indx3 = Nt-1\n",
"\n",
" t1 = t[indx1]\n",
" t2 = t[indx2]\n",
" t3 = t[indx3]\n",
"\n",
" # Slice the results from the DNN\n",
" res1 = res[:,indx1]\n",
" res2 = res[:,indx2]\n",
" res3 = res[:,indx3]\n",
"\n",
" # Slice the analytical results\n",
" res_analytical1 = res_analytical[:,indx1]\n",
" res_analytical2 = res_analytical[:,indx2]\n",
" res_analytical3 = res_analytical[:,indx3]\n",
"\n",
" # Plot the slices\n",
" plt.figure(figsize=(10,10))\n",
" plt.title(\"Computed solutions at time = %g\"%t1)\n",
" plt.plot(x, res1)\n",
" plt.plot(x,res_analytical1)\n",
" plt.legend(['dnn','analytical'])\n",
"\n",
" plt.figure(figsize=(10,10))\n",
" plt.title(\"Computed solutions at time = %g\"%t2)\n",
" plt.plot(x, res2)\n",
" plt.plot(x,res_analytical2)\n",
" plt.legend(['dnn','analytical'])\n",
"\n",
" plt.figure(figsize=(10,10))\n",
" plt.title(\"Computed solutions at time = %g\"%t3)\n",
" plt.plot(x, res3)\n",
" plt.plot(x,res_analytical3)\n",
" plt.legend(['dnn','analytical'])\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "a23bd19a",
"metadata": {
"editable": true
},
"source": [
"## Resources on differential equations and deep learning\n",
"\n",
"1. [Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al](https://pdfs.semanticscholar.org/d061/df393e0e8fbfd0ea24976458b7d42419040d.pdf)\n",
"\n",
"2. [Neural networks for solving differential equations by A. Honchar](https://becominghuman.ai/neural-networks-for-solving-differential-equations-fa230ac5e04c)\n",
"\n",
"3. [Solving differential equations using neural networks by M.M Chiaramonte and M. Kiener](http://cs229.stanford.edu/proj2013/ChiaramonteKiener-SolvingDifferentialEquationsUsingNeuralNetworks.pdf)\n",
"\n",
"4. [Introduction to Partial Differential Equations by A. Tveito, R. Winther](https://www.springer.com/us/book/9783540225515)"
]
}
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