From 4f225ce503fc92d28f198a3b74d96747b2314fdc Mon Sep 17 00:00:00 2001 From: mhjensen Date: Fri, 28 Sep 2018 11:14:05 +0200 Subject: [PATCH] update on neural nets --- doc/pub/LogReg/ipynb/LogReg.ipynb | 28 +- doc/pub/NeuralNet/html/NeuralNet-bs.html | 166 ++- doc/pub/NeuralNet/html/NeuralNet-reveal.html | 108 +- .../NeuralNet/html/NeuralNet-solarized.html | 132 +-- doc/pub/NeuralNet/html/NeuralNet.html | 132 +-- doc/pub/NeuralNet/ipynb/NeuralNet.ipynb | 63 +- .../ipynb/ipynb-NeuralNet-src.tar.gz | Bin 211 -> 209 bytes .../pdf/NeuralNet-beamer-handouts2x3.pdf | Bin 287702 -> 286587 bytes doc/pub/NeuralNet/pdf/NeuralNet-beamer.pdf | Bin 270607 -> 269549 bytes doc/pub/NeuralNet/pdf/NeuralNet-minted.pdf | Bin 352420 -> 350200 bytes doc/pub/Splines/ipynb/Splines.ipynb | 241 ++-- doc/src/NeuralNet/NeuralNet.do.txt | 66 +- doc/src/NeuralNet/diffeq.tex | 1047 ----------------- 13 files changed, 455 insertions(+), 1528 deletions(-) delete mode 100644 doc/src/NeuralNet/diffeq.tex diff --git a/doc/pub/LogReg/ipynb/LogReg.ipynb b/doc/pub/LogReg/ipynb/LogReg.ipynb index 43615a1d1..baaa9264e 100644 --- a/doc/pub/LogReg/ipynb/LogReg.ipynb +++ b/doc/pub/LogReg/ipynb/LogReg.ipynb @@ -388,9 +388,7 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", @@ -425,9 +423,7 @@ { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -482,7 +478,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.0" + } + }, "nbformat": 4, "nbformat_minor": 2 } diff --git a/doc/pub/NeuralNet/html/NeuralNet-bs.html b/doc/pub/NeuralNet/html/NeuralNet-bs.html index c35fba36f..a38909828 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-bs.html +++ b/doc/pub/NeuralNet/html/NeuralNet-bs.html @@ -40,28 +40,31 @@ Automatically generated HTML file from DocOnce source @@ -100,25 +103,25 @@ MathJax.Hub.Config({
  • Contents @@ -153,59 +156,32 @@ MathJax.Hub.Config({
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    May 30, 2018

    +

    Sep 28, 2018


    +

    + +

    -

    What is Machine Learning?

    +

    Neural networks

    -Machine learning is the science of giving computers the ability to -learn without being explicitly programmed. The idea is that there -exist generic algorithms which can be used to find patterns in a broad -class of data sets without having to write code specifically for each -problem. The algorithm will build its own logic based on the data. - -

    -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. It has also, especially in later -years, found applications in a wide variety of other areas, including -bioinformatics, economy, physics, finance and marketing. +Artificial neural networks are computational systems that can learn to +perform tasks by considering examples, generally without being +programmed with any task-specific rules. It is supposed to mimic a +biological system, wherein neurons interact by sending signals in the +form of mathematical functions between layers. All layers can contain +an arbitrary number of neurons, and each connection is represented by +a weight variable.

    -

    Types of Machine Learning

    - -

    -The approaches to machine learning are many, but are often split into two main categories. -In supervised learning we know the answer to a problem, -and let the computer deduce the logic behind it. On the other hand, unsupervised learning -is a method for finding patterns and relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely reinforcement learning. This is a paradigm -of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. - -

    -Another way to categorize machine learning tasks is to consider the desired output of a system. -Some of the most common tasks are: - -

    - - - -

    Artificial neurons

    +

    Artificial neurons

    The field of artificial neural networks has a long history of @@ -244,13 +220,13 @@ categories:

  • neural networks for unsupervised learning such as Deep Boltzmann Machines.
    • -In physics, DNNs and CNNs have already found numerous applications. In +In natural science, DNNs and CNNs have already found numerous applications. In statistical physics, they have been applied to detect phase transitions in 2D Ising and Potts models, lattice gauge theories, and -different phases of polymers. +different phases of polymers, or solving the Navier-Stokes equation in weather forecasting. Deep learning has also found interesting applications in quantum physics. Various quantum phase transitions can be detected and studied -using DNNs and CNNs, including the transverse-field Ising model, +using DNNs and CNNs, topological phases, and even non-equilibrium many-body localization. Representing quantum states as DNNs quantum state tomography are among some of the impressive @@ -261,14 +237,15 @@ of quantum systems. In quantum information theory, it has been shown that one can perform gate decompositions with the help of neural. In lattice quantum chromodynamics, DNNs have been used to learn action parameters in regions of parameter -space where PCA fails. Last but not least, -DNNs also found place in the study of quantum, and in scattering theory to learn -\( s \)-wave scattering length of potentials. +space where PCA fails. + +

    +The applications are not limited to the natural sciences. There is a plethora of applications in essentially all disciplines, from the humanities to life science and medicine.

    -

    Neural network types

    +

    Neural network types

    An artificial neural network (NN), is a computational model that @@ -291,7 +268,7 @@ methods.

    -

    Feed-forward neural networks

    +

    Feed-forward neural networks

    The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, @@ -322,7 +299,7 @@ which gathers all the local data and produces the outputs. They have wide applic

    -

    Recurrent neural networks

    +

    Recurrent neural networks

    So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on @@ -335,7 +312,7 @@ sentences, making recurrent NNs especially well-suited for handwriting and speec

    -

    Other types of networks

    +

    Other types of networks

    There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation @@ -352,7 +329,7 @@ of how a fully-connected FFNN works, and how it can be used to interpolate data

    -

    Multilayer perceptrons

    +

    Multilayer perceptrons

    One use often so-called fully-connected feed-forward neural networks with three @@ -365,7 +342,7 @@ Such networks are often called multilayer perceptrons (MLPs)

    -

    Why multilayer perceptrons?

    +

    Why multilayer perceptrons?

    According to the Universal approximation theorem, a feed-forward neural network with just a single hidden layer containing @@ -386,7 +363,7 @@ functions.

    -

    Mathematical model

    +

    Mathematical model

    $$ \begin{equation} @@ -402,7 +379,7 @@ which means that each neuron receives a weighted sum of the outputs of all -

    Mathematical model

    +

    Mathematical model

    First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), @@ -439,7 +416,7 @@ the values of the subsequent layer can be calculated and so forth until the outp

    -

    Mathematical model

    +

    Mathematical model

    The output of neuron \( i \) in layer 2 is thus, @@ -468,7 +445,7 @@ $$

    -

    Mathematical model

    +

    Mathematical model

    We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form @@ -488,7 +465,7 @@ which illustrates a basic property of MLPs: The only independent variables are t

    -

    Mathematical model

    +

    Mathematical model

    This confirms that an MLP, @@ -515,7 +492,7 @@ which is the key to the flexibility of a neural network.

    -

    Matrix-vector notation

    +

    Matrix-vector notation

    We can introduce a more convenient notation for the activations in a NN. @@ -553,7 +530,7 @@ $$

    -

    Matrix-vector notation and activation

    +

    Matrix-vector notation and activation

    The activation of node \( i \) in layer 2 is @@ -573,7 +550,7 @@ and vector additions that are used as input to the activation functions. For eac

    -

    Activation functions

    +

    Activation functions

    A property that characterizes a neural network, other than its connectivity, is the choice of activation function(s). @@ -589,7 +566,7 @@ to fulfill the universal approximation theorem -

    Activation functions, Logistic and Hyperbolic ones

    +

    Activation functions, Logistic and Hyperbolic ones

    The second requirement excludes all linear functions. Furthermore, in a MLP with only linear activation functions, each @@ -618,7 +595,7 @@ $$

    -

    Relevance

    +

    Relevance

    The sigmoid function are more biologically plausible because the output of inactive neurons are zero. Such activation function are called one-sided. However, @@ -701,6 +678,11 @@ ax.set_title(&# plt.show() +

    + + +

    Setting up a Multi-layer perceptron model

    +

    diff --git a/doc/pub/NeuralNet/html/NeuralNet-reveal.html b/doc/pub/NeuralNet/html/NeuralNet-reveal.html index a14532bdb..99cb9c0d8 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-reveal.html +++ b/doc/pub/NeuralNet/html/NeuralNet-reveal.html @@ -148,8 +148,11 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

     
    -

    May 30, 2018

    +

    Sep 28, 2018


    +

    + +

    @@ -159,55 +162,21 @@ MathJax.Hub.Config({
    -

    What is Machine Learning?

    +

    Neural networks

    -Machine learning is the science of giving computers the ability to -learn without being explicitly programmed. The idea is that there -exist generic algorithms which can be used to find patterns in a broad -class of data sets without having to write code specifically for each -problem. The algorithm will build its own logic based on the data. - -

    -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. It has also, especially in later -years, found applications in a wide variety of other areas, including -bioinformatics, economy, physics, finance and marketing. +Artificial neural networks are computational systems that can learn to +perform tasks by considering examples, generally without being +programmed with any task-specific rules. It is supposed to mimic a +biological system, wherein neurons interact by sending signals in the +form of mathematical functions between layers. All layers can contain +an arbitrary number of neurons, and each connection is represented by +a weight variable.

    -

    Types of Machine Learning

    - -

    -The approaches to machine learning are many, but are often split into two main categories. -In supervised learning we know the answer to a problem, -and let the computer deduce the logic behind it. On the other hand, unsupervised learning -is a method for finding patterns and relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely reinforcement learning. This is a paradigm -of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. - -

    -Another way to categorize machine learning tasks is to consider the desired output of a system. -Some of the most common tasks are: - -

      - -

    • Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.
      • - -

    • Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.
      • - -

    • Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
      • -
    -
    - - -
    -

    Artificial neurons

    +

    Artificial neurons

    The field of artificial neural networks has a long history of @@ -249,13 +218,13 @@ categories:

    -In physics, DNNs and CNNs have already found numerous applications. In +In natural science, DNNs and CNNs have already found numerous applications. In statistical physics, they have been applied to detect phase transitions in 2D Ising and Potts models, lattice gauge theories, and -different phases of polymers. +different phases of polymers, or solving the Navier-Stokes equation in weather forecasting. Deep learning has also found interesting applications in quantum physics. Various quantum phase transitions can be detected and studied -using DNNs and CNNs, including the transverse-field Ising model, +using DNNs and CNNs, topological phases, and even non-equilibrium many-body localization. Representing quantum states as DNNs quantum state tomography are among some of the impressive @@ -266,14 +235,15 @@ of quantum systems. In quantum information theory, it has been shown that one can perform gate decompositions with the help of neural. In lattice quantum chromodynamics, DNNs have been used to learn action parameters in regions of parameter -space where PCA fails. Last but not least, -DNNs also found place in the study of quantum, and in scattering theory to learn -\( s \)-wave scattering length of potentials. +space where PCA fails. + +

    +The applications are not limited to the natural sciences. There is a plethora of applications in essentially all disciplines, from the humanities to life science and medicine.

    -

    Neural network types

    +

    Neural network types

    An artificial neural network (NN), is a computational model that @@ -296,7 +266,7 @@ methods.

    -

    Feed-forward neural networks

    +

    Feed-forward neural networks

    The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, @@ -327,7 +297,7 @@ which gathers all the local data and produces the outputs. They have wide applic

    -

    Recurrent neural networks

    +

    Recurrent neural networks

    So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on @@ -340,7 +310,7 @@ sentences, making recurrent NNs especially well-suited for handwriting and speec

    -

    Other types of networks

    +

    Other types of networks

    There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation @@ -357,7 +327,7 @@ of how a fully-connected FFNN works, and how it can be used to interpolate data

    -

    Multilayer perceptrons

    +

    Multilayer perceptrons

    One use often so-called fully-connected feed-forward neural networks with three @@ -370,7 +340,7 @@ Such networks are often called multilayer perceptrons (MLPs)

    -

    Why multilayer perceptrons?

    +

    Why multilayer perceptrons?

    According to the Universal approximation theorem, a feed-forward neural network with just a single hidden layer containing @@ -391,7 +361,7 @@ functions.

    -

    Mathematical model

    +

    Mathematical model

     
    $$ @@ -409,7 +379,7 @@ which means that each neuron receives a weighted sum of the outputs of all -

    Mathematical model

    +

    Mathematical model

    First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), @@ -452,7 +422,7 @@ the values of the subsequent layer can be calculated and so forth until the outp

    -

    Mathematical model

    +

    Mathematical model

    The output of neuron \( i \) in layer 2 is thus, @@ -485,7 +455,7 @@ $$

    -

    Mathematical model

    +

    Mathematical model

    We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form @@ -507,7 +477,7 @@ which illustrates a basic property of MLPs: The only independent variables are t

    -

    Mathematical model

    +

    Mathematical model

    This confirms that an MLP, @@ -537,7 +507,7 @@ which is the key to the flexibility of a neural network.

    -

    Matrix-vector notation

    +

    Matrix-vector notation

    We can introduce a more convenient notation for the activations in a NN. @@ -578,7 +548,7 @@ $$
    -

    Matrix-vector notation and activation

    +

    Matrix-vector notation and activation

    The activation of node \( i \) in layer 2 is @@ -601,7 +571,7 @@ and vector additions that are used as input to the activation functions. For eac
    -

    Activation functions

    +

    Activation functions

    A property that characterizes a neural network, other than its connectivity, is the choice of activation function(s). @@ -623,7 +593,7 @@ to fulfill the universal approximation theorem

    -

    Activation functions, Logistic and Hyperbolic ones

    +

    Activation functions, Logistic and Hyperbolic ones

    The second requirement excludes all linear functions. Furthermore, in a MLP with only linear activation functions, each @@ -657,7 +627,7 @@ $$

    -

    Relevance

    +

    Relevance

    The sigmoid function are more biologically plausible because the output of inactive neurons are zero. Such activation function are called one-sided. However, @@ -740,6 +710,12 @@ ax.set_title('Rectified linear unit' plt.show() +
    + + +
    +

    Setting up a Multi-layer perceptron model

    +

    diff --git a/doc/pub/NeuralNet/html/NeuralNet-solarized.html b/doc/pub/NeuralNet/html/NeuralNet-solarized.html index b86329bed..eccecb928 100644 --- a/doc/pub/NeuralNet/html/NeuralNet-solarized.html +++ b/doc/pub/NeuralNet/html/NeuralNet-solarized.html @@ -34,28 +34,31 @@ div { text-align: justify; text-justify: inter-word; } @@ -98,56 +101,29 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    May 30, 2018

    +

    Sep 28, 2018


    -









    - -

    What is Machine Learning?

    - -

    -Machine learning is the science of giving computers the ability to -learn without being explicitly programmed. The idea is that there -exist generic algorithms which can be used to find patterns in a broad -class of data sets without having to write code specifically for each -problem. The algorithm will build its own logic based on the data. - -

    -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. It has also, especially in later -years, found applications in a wide variety of other areas, including -bioinformatics, economy, physics, finance and marketing. +











    -

    Types of Machine Learning

    +

    Neural networks

    -The approaches to machine learning are many, but are often split into two main categories. -In supervised learning we know the answer to a problem, -and let the computer deduce the logic behind it. On the other hand, unsupervised learning -is a method for finding patterns and relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely reinforcement learning. This is a paradigm -of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. +Artificial neural networks are computational systems that can learn to +perform tasks by considering examples, generally without being +programmed with any task-specific rules. It is supposed to mimic a +biological system, wherein neurons interact by sending signals in the +form of mathematical functions between layers. All layers can contain +an arbitrary number of neurons, and each connection is represented by +a weight variable.

    -Another way to categorize machine learning tasks is to consider the desired output of a system. -Some of the most common tasks are: - -

      -
    • Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.
      • -
    • Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.
      • -
    • Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
      • -
    -









    -

    Artificial neurons

    +

    Artificial neurons

    The field of artificial neural networks has a long history of @@ -186,13 +162,13 @@ categories:

  • neural networks for unsupervised learning such as Deep Boltzmann Machines.
    • -In physics, DNNs and CNNs have already found numerous applications. In +In natural science, DNNs and CNNs have already found numerous applications. In statistical physics, they have been applied to detect phase transitions in 2D Ising and Potts models, lattice gauge theories, and -different phases of polymers. +different phases of polymers, or solving the Navier-Stokes equation in weather forecasting. Deep learning has also found interesting applications in quantum physics. Various quantum phase transitions can be detected and studied -using DNNs and CNNs, including the transverse-field Ising model, +using DNNs and CNNs, topological phases, and even non-equilibrium many-body localization. Representing quantum states as DNNs quantum state tomography are among some of the impressive @@ -203,14 +179,15 @@ of quantum systems. In quantum information theory, it has been shown that one can perform gate decompositions with the help of neural. In lattice quantum chromodynamics, DNNs have been used to learn action parameters in regions of parameter -space where PCA fails. Last but not least, -DNNs also found place in the study of quantum, and in scattering theory to learn -\( s \)-wave scattering length of potentials. +space where PCA fails. + +

    +The applications are not limited to the natural sciences. There is a plethora of applications in essentially all disciplines, from the humanities to life science and medicine.











    -

    Neural network types

    +

    Neural network types

    An artificial neural network (NN), is a computational model that @@ -233,7 +210,7 @@ methods.











    -

    Feed-forward neural networks

    +

    Feed-forward neural networks

    The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, @@ -264,7 +241,7 @@ which gathers all the local data and produces the outputs. They have wide applic











    -

    Recurrent neural networks

    +

    Recurrent neural networks

    So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on @@ -277,7 +254,7 @@ sentences, making recurrent NNs especially well-suited for handwriting and speec











    -

    Other types of networks

    +

    Other types of networks

    There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation @@ -294,7 +271,7 @@ of how a fully-connected FFNN works, and how it can be used to interpolate data











    -

    Multilayer perceptrons

    +

    Multilayer perceptrons

    One use often so-called fully-connected feed-forward neural networks with three @@ -307,7 +284,7 @@ Such networks are often called multilayer perceptrons (MLPs)











    -

    Why multilayer perceptrons?

    +

    Why multilayer perceptrons?

    According to the Universal approximation theorem, a feed-forward neural network with just a single hidden layer containing @@ -328,7 +305,7 @@ functions.











    -

    Mathematical model

    +

    Mathematical model

    $$ \begin{equation} @@ -344,7 +321,7 @@ which means that each neuron receives a weighted sum of the outputs of all









    -

    Mathematical model

    +

    Mathematical model

    First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), @@ -381,7 +358,7 @@ the values of the subsequent layer can be calculated and so forth until the outp











    -

    Mathematical model

    +

    Mathematical model

    The output of neuron \( i \) in layer 2 is thus, @@ -410,7 +387,7 @@ $$











    -

    Mathematical model

    +

    Mathematical model

    We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form @@ -430,7 +407,7 @@ which illustrates a basic property of MLPs: The only independent variables are t











    -

    Mathematical model

    +

    Mathematical model

    This confirms that an MLP, @@ -457,7 +434,7 @@ which is the key to the flexibility of a neural network.











    -

    Matrix-vector notation

    +

    Matrix-vector notation

    We can introduce a more convenient notation for the activations in a NN. @@ -495,7 +472,7 @@ $$











    -

    Matrix-vector notation and activation

    +

    Matrix-vector notation and activation

    The activation of node \( i \) in layer 2 is @@ -515,7 +492,7 @@ and vector additions that are used as input to the activation functions. For eac











    -

    Activation functions

    +

    Activation functions

    A property that characterizes a neural network, other than its connectivity, is the choice of activation function(s). @@ -531,7 +508,7 @@ to fulfill the universal approximation theorem









    -

    Activation functions, Logistic and Hyperbolic ones

    +

    Activation functions, Logistic and Hyperbolic ones

    The second requirement excludes all linear functions. Furthermore, in a MLP with only linear activation functions, each @@ -560,7 +537,7 @@ $$











    -

    Relevance

    +

    Relevance

    The sigmoid function are more biologically plausible because the output of inactive neurons are zero. Such activation function are called one-sided. However, @@ -643,6 +620,11 @@ ax.set_title('Rectified linear unit' plt.show() +

    + + +

    Setting up a Multi-layer perceptron model

    +

    diff --git a/doc/pub/NeuralNet/html/NeuralNet.html b/doc/pub/NeuralNet/html/NeuralNet.html index e70181f2c..b01022ab1 100644 --- a/doc/pub/NeuralNet/html/NeuralNet.html +++ b/doc/pub/NeuralNet/html/NeuralNet.html @@ -39,28 +39,31 @@ div { text-align: justify; text-justify: inter-word; } @@ -103,56 +106,29 @@ MathJax.Hub.Config({

    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

    -

    May 30, 2018

    +

    Sep 28, 2018


    -









    - -

    What is Machine Learning?

    - -

    -Machine learning is the science of giving computers the ability to -learn without being explicitly programmed. The idea is that there -exist generic algorithms which can be used to find patterns in a broad -class of data sets without having to write code specifically for each -problem. The algorithm will build its own logic based on the data. - -

    -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. It has also, especially in later -years, found applications in a wide variety of other areas, including -bioinformatics, economy, physics, finance and marketing. +











    -

    Types of Machine Learning

    +

    Neural networks

    -The approaches to machine learning are many, but are often split into two main categories. -In supervised learning we know the answer to a problem, -and let the computer deduce the logic behind it. On the other hand, unsupervised learning -is a method for finding patterns and relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely reinforcement learning. This is a paradigm -of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. +Artificial neural networks are computational systems that can learn to +perform tasks by considering examples, generally without being +programmed with any task-specific rules. It is supposed to mimic a +biological system, wherein neurons interact by sending signals in the +form of mathematical functions between layers. All layers can contain +an arbitrary number of neurons, and each connection is represented by +a weight variable.

    -Another way to categorize machine learning tasks is to consider the desired output of a system. -Some of the most common tasks are: - -

      -
    • Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.
      • -
    • Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.
      • -
    • Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.
      • -
    -









    -

    Artificial neurons

    +

    Artificial neurons

    The field of artificial neural networks has a long history of @@ -191,13 +167,13 @@ categories:

  • neural networks for unsupervised learning such as Deep Boltzmann Machines.
    • -In physics, DNNs and CNNs have already found numerous applications. In +In natural science, DNNs and CNNs have already found numerous applications. In statistical physics, they have been applied to detect phase transitions in 2D Ising and Potts models, lattice gauge theories, and -different phases of polymers. +different phases of polymers, or solving the Navier-Stokes equation in weather forecasting. Deep learning has also found interesting applications in quantum physics. Various quantum phase transitions can be detected and studied -using DNNs and CNNs, including the transverse-field Ising model, +using DNNs and CNNs, topological phases, and even non-equilibrium many-body localization. Representing quantum states as DNNs quantum state tomography are among some of the impressive @@ -208,14 +184,15 @@ of quantum systems. In quantum information theory, it has been shown that one can perform gate decompositions with the help of neural. In lattice quantum chromodynamics, DNNs have been used to learn action parameters in regions of parameter -space where PCA fails. Last but not least, -DNNs also found place in the study of quantum, and in scattering theory to learn -\( s \)-wave scattering length of potentials. +space where PCA fails. + +

    +The applications are not limited to the natural sciences. There is a plethora of applications in essentially all disciplines, from the humanities to life science and medicine.











    -

    Neural network types

    +

    Neural network types

    An artificial neural network (NN), is a computational model that @@ -238,7 +215,7 @@ methods.











    -

    Feed-forward neural networks

    +

    Feed-forward neural networks

    The feed-forward neural network (FFNN) was the first and simplest type of NN devised. In this network, @@ -269,7 +246,7 @@ which gathers all the local data and produces the outputs. They have wide applic











    -

    Recurrent neural networks

    +

    Recurrent neural networks

    So far we have only mentioned NNs where information flows in one direction: forward. Recurrent neural networks on @@ -282,7 +259,7 @@ sentences, making recurrent NNs especially well-suited for handwriting and speec











    -

    Other types of networks

    +

    Other types of networks

    There are many other kinds of NNs that have been developed. One type that is specifically designed for interpolation @@ -299,7 +276,7 @@ of how a fully-connected FFNN works, and how it can be used to interpolate data











    -

    Multilayer perceptrons

    +

    Multilayer perceptrons

    One use often so-called fully-connected feed-forward neural networks with three @@ -312,7 +289,7 @@ Such networks are often called multilayer perceptrons (MLPs)











    -

    Why multilayer perceptrons?

    +

    Why multilayer perceptrons?

    According to the Universal approximation theorem, a feed-forward neural network with just a single hidden layer containing @@ -333,7 +310,7 @@ functions.











    -

    Mathematical model

    +

    Mathematical model

    $$ \begin{equation} @@ -349,7 +326,7 @@ which means that each neuron receives a weighted sum of the outputs of all









    -

    Mathematical model

    +

    Mathematical model

    First, for each node \( i \) in the first hidden layer, we calculate a weighted sum \( u_i^1 \) of the input coordinates \( x_j \), @@ -386,7 +363,7 @@ the values of the subsequent layer can be calculated and so forth until the outp











    -

    Mathematical model

    +

    Mathematical model

    The output of neuron \( i \) in layer 2 is thus, @@ -415,7 +392,7 @@ $$











    -

    Mathematical model

    +

    Mathematical model

    We can generalize this expression to an MLP with \( l \) hidden layers. The complete functional form @@ -435,7 +412,7 @@ which illustrates a basic property of MLPs: The only independent variables are t











    -

    Mathematical model

    +

    Mathematical model

    This confirms that an MLP, @@ -462,7 +439,7 @@ which is the key to the flexibility of a neural network.











    -

    Matrix-vector notation

    +

    Matrix-vector notation

    We can introduce a more convenient notation for the activations in a NN. @@ -500,7 +477,7 @@ $$











    -

    Matrix-vector notation and activation

    +

    Matrix-vector notation and activation

    The activation of node \( i \) in layer 2 is @@ -520,7 +497,7 @@ and vector additions that are used as input to the activation functions. For eac











    -

    Activation functions

    +

    Activation functions

    A property that characterizes a neural network, other than its connectivity, is the choice of activation function(s). @@ -536,7 +513,7 @@ to fulfill the universal approximation theorem









    -

    Activation functions, Logistic and Hyperbolic ones

    +

    Activation functions, Logistic and Hyperbolic ones

    The second requirement excludes all linear functions. Furthermore, in a MLP with only linear activation functions, each @@ -565,7 +542,7 @@ $$











    -

    Relevance

    +

    Relevance

    The sigmoid function are more biologically plausible because the output of inactive neurons are zero. Such activation function are called one-sided. However, @@ -648,6 +625,11 @@ ax.set_title(&# plt.show() +

    + + +

    Setting up a Multi-layer perceptron model

    +

    diff --git a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb index d83a1f311..5665fe4cd 100644 --- a/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb +++ b/doc/pub/NeuralNet/ipynb/NeuralNet.ipynb @@ -10,47 +10,24 @@ " \n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n", "\n", - "Date: **May 30, 2018**\n", + "Date: **Sep 28, 2018**\n", "\n", "Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n", "\n", "\n", "\n", - "## What is Machine Learning?\n", + "\n", "\n", - "Machine learning is the science of giving computers the ability to\n", - "learn without being explicitly programmed. The idea is that there\n", - "exist generic algorithms which can be used to find patterns in a broad\n", - "class of data sets without having to write code specifically for each\n", - "problem. The algorithm will build its own logic based on the data.\n", + "## Neural networks\n", "\n", - "Machine learning is a subfield of computer science, and is closely\n", - "related to computational statistics. It evolved from the study of\n", - "pattern recognition in artificial intelligence (AI) research, and has\n", - "made contributions to AI tasks like computer vision, natural language\n", - "processing and speech recognition. It has also, especially in later\n", - "years, found applications in a wide variety of other areas, including\n", - "bioinformatics, economy, physics, finance and marketing.\n", + "Artificial neural networks are computational systems that can learn to\n", + "perform tasks by considering examples, generally without being\n", + "programmed with any task-specific rules. It is supposed to mimic a\n", + "biological system, wherein neurons interact by sending signals in the\n", + "form of mathematical functions between layers. All layers can contain\n", + "an arbitrary number of neurons, and each connection is represented by\n", + "a weight variable.\n", "\n", - "## Types of Machine Learning\n", - "\n", - "\n", - "The approaches to machine learning are many, but are often split into two main categories. \n", - "In *supervised learning* we know the answer to a problem,\n", - "and let the computer deduce the logic behind it. On the other hand, *unsupervised learning*\n", - "is a method for finding patterns and relationship in data sets without any prior knowledge of the system.\n", - "Some authours also operate with a third category, namely *reinforcement learning*. This is a paradigm \n", - "of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, \n", - "solely from rewards and punishment.\n", - "\n", - "Another way to categorize machine learning tasks is to consider the desired output of a system.\n", - "Some of the most common tasks are:\n", - "\n", - " * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.\n", - "\n", - " * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.\n", - "\n", - " * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.\n", "\n", "## Artificial neurons\n", "\n", @@ -101,13 +78,13 @@ "\n", "4. neural networks for unsupervised learning such as Deep Boltzmann Machines.\n", "\n", - "In physics, DNNs and CNNs have already found numerous applications. In\n", + "In natural science, DNNs and CNNs have already found numerous applications. In\n", "statistical physics, they have been applied to detect phase\n", "transitions in 2D Ising and Potts models, lattice gauge theories, and\n", - "different phases of polymers.\n", + "different phases of polymers, or solving the Navier-Stokes equation in weather forecasting.\n", "Deep learning has also found interesting applications in quantum\n", "physics. Various quantum phase transitions can be detected and studied\n", - "using DNNs and CNNs, including the transverse-field Ising model,\n", + "using DNNs and CNNs,\n", "topological phases, and even non-equilibrium many-body\n", "localization. Representing quantum states as DNNs quantum state\n", "tomography are among some of the impressive\n", @@ -117,9 +94,9 @@ "In quantum information theory, it has been shown that one can perform\n", "gate decompositions with the help of neural. In lattice quantum chromodynamics,\n", "DNNs have been used to learn action parameters in regions of parameter\n", - "space where PCA fails. Last but not least,\n", - "DNNs also found place in the study of quantum, and in scattering theory to learn\n", - "$s$-wave scattering length of potentials.\n", + "space where PCA fails. \n", + "\n", + "The applications are not limited to the natural sciences. There is a plethora of applications in essentially all disciplines, from the humanities to life science and medicine.\n", "\n", "## Neural network types\n", "\n", @@ -692,6 +669,14 @@ "plt.show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "## Setting up a Multi-layer perceptron model" + ] + }, { "cell_type": "code", "execution_count": 2, diff --git a/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz b/doc/pub/NeuralNet/ipynb/ipynb-NeuralNet-src.tar.gz index 07d85754a0ed0039cd23a1320660b486bdea2c5a..b35e004cf669ad43ea0b804a55c83fdbac1e50e8 100644 GIT binary patch literal 209 zcmb2|=3rp>ur`{3`R)0GSxkl^t%=v|j@C9Q&I-KF8e0-5_>omf*gDhnq6+i5+t!OO zth+V0<467M!-~@j-dBAz`yV0la}Im?;wiJHE&XCS+i%^_d-m*gaE_xhV!yXoKgoq0Lie?OmpTl3Ro|D@pED(_dDT|d~(e>2bd$F!xn zi*D-Y>fPD+HF{-}@88uf)mbrHl4`V^#A|> literal 211 zcmb2|=3tnS!XM4R{Pz68tV0e0#|qEe9kp?km~3Jz{^f$R>k|D9leXRrD=#f)e)d*c z^j2{7%VZCVpj zqLVeZ#Gm zQfsn%>Dg9mo;u~+4KMFZ&FJ6T9o8d%WXsyqdKH^z%OzEGr_Jwr8ULS|0U3OMBz&xD 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z$%mxnMnnCJ+1kcEX71fM)6?0{ZEmtA1xsj?B`@8q2@_&YN*F{M0tMW^ud1g8_%9Oe B*FXRO diff --git a/doc/pub/Splines/ipynb/Splines.ipynb b/doc/pub/Splines/ipynb/Splines.ipynb index 805fb1f6d..350eb63c0 100644 --- a/doc/pub/Splines/ipynb/Splines.ipynb +++ b/doc/pub/Splines/ipynb/Splines.ipynb @@ -844,10 +844,29 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": false - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
      " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)\n", @@ -903,9 +931,7 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "x = guesses[-1]\n", @@ -922,10 +948,16 @@ { "cell_type": "code", "execution_count": 4, - "metadata": { - "collapsed": false - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.33333333 -0.26666667]\n" + ] + } + ], "source": [ "def f1d(alpha):\n", " return f(x + alpha*s)\n", @@ -946,10 +978,29 @@ { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": false - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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      " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh, 50)\n", @@ -1140,9 +1191,7 @@ { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -1176,11 +1225,30 @@ }, { "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[3.96812677]\n", + " [2.93472871]]\n", + "[[3.96812677]\n", + " [2.93472871]]\n" + ] + }, + { + "data": { + "image/png": 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\n", 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      " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "# Importing various packages\n", @@ -1233,9 +1301,7 @@ { "cell_type": "code", "execution_count": 8, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "# Importing various packages\n", @@ -1319,9 +1385,7 @@ { "cell_type": "code", "execution_count": 9, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -1394,11 +1458,27 @@ }, { "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
      " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max absolute difference is: 1.77636e-15\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "\n", @@ -1452,11 +1532,18 @@ }, { "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": false - }, - "outputs": [], + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f1 evaluated at a = 1 using autograd is: 3\n", + "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -1491,9 +1578,7 @@ { "cell_type": "code", "execution_count": 12, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1544,9 +1629,7 @@ { "cell_type": "code", "execution_count": 13, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1586,9 +1669,7 @@ { "cell_type": "code", "execution_count": 14, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1620,9 +1701,7 @@ { "cell_type": "code", "execution_count": 15, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1682,9 +1761,7 @@ { "cell_type": "code", "execution_count": 16, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1708,9 +1785,7 @@ { "cell_type": "code", "execution_count": 17, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1757,9 +1832,7 @@ { "cell_type": "code", "execution_count": 18, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1787,9 +1860,7 @@ { "cell_type": "code", "execution_count": 19, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1817,9 +1888,7 @@ { "cell_type": "code", "execution_count": 20, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -1849,9 +1918,7 @@ { "cell_type": "code", "execution_count": 21, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "a += b\n", @@ -1976,9 +2043,7 @@ { "cell_type": "code", "execution_count": 22, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -2040,9 +2105,7 @@ { "cell_type": "code", "execution_count": 23, - "metadata": { - "collapsed": false - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -2072,7 +2135,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.0" + } + }, "nbformat": 4, "nbformat_minor": 2 } diff --git a/doc/src/NeuralNet/NeuralNet.do.txt b/doc/src/NeuralNet/NeuralNet.do.txt index bc144526d..99bd95258 100644 --- a/doc/src/NeuralNet/NeuralNet.do.txt +++ b/doc/src/NeuralNet/NeuralNet.do.txt @@ -5,42 +5,15 @@ DATE: today # add own code for DNN !split -===== What is Machine Learning? ===== +===== Neural networks ===== -Machine learning is the science of giving computers the ability to -learn without being explicitly programmed. The idea is that there -exist generic algorithms which can be used to find patterns in a broad -class of data sets without having to write code specifically for each -problem. The algorithm will build its own logic based on the data. - -Machine learning is a subfield of computer science, and is closely -related to computational statistics. It evolved from the study of -pattern recognition in artificial intelligence (AI) research, and has -made contributions to AI tasks like computer vision, natural language -processing and speech recognition. It has also, especially in later -years, found applications in a wide variety of other areas, including -bioinformatics, economy, physics, finance and marketing. - -!split -===== Types of Machine Learning ===== - - -The approaches to machine learning are many, but are often split into two main categories. -In *supervised learning* we know the answer to a problem, -and let the computer deduce the logic behind it. On the other hand, *unsupervised learning* -is a method for finding patterns and relationship in data sets without any prior knowledge of the system. -Some authours also operate with a third category, namely *reinforcement learning*. This is a paradigm -of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, -solely from rewards and punishment. - -Another way to categorize machine learning tasks is to consider the desired output of a system. -Some of the most common tasks are: - - * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning. - - * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values. - - * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning. +Artificial neural networks are computational systems that can learn to +perform tasks by considering examples, generally without being +programmed with any task-specific rules. It is supposed to mimic a +biological system, wherein neurons interact by sending signals in the +form of mathematical functions between layers. All layers can contain +an arbitrary number of neurons, and each connection is represented by +a weight variable. !split @@ -77,13 +50,13 @@ o neural networks for sequential data such as Recurrent Neural Networks (RNNs), o neural networks for unsupervised learning such as Deep Boltzmann Machines. -In physics, DNNs and CNNs have already found numerous applications. In +In natural science, DNNs and CNNs have already found numerous applications. In statistical physics, they have been applied to detect phase transitions in 2D Ising and Potts models, lattice gauge theories, and -different phases of polymers. +different phases of polymers, or solving the Navier-Stokes equation in weather forecasting. Deep learning has also found interesting applications in quantum physics. Various quantum phase transitions can be detected and studied -using DNNs and CNNs, including the transverse-field Ising model, +using DNNs and CNNs, topological phases, and even non-equilibrium many-body localization. Representing quantum states as DNNs quantum state tomography are among some of the impressive @@ -93,9 +66,9 @@ of quantum systems. In quantum information theory, it has been shown that one can perform gate decompositions with the help of neural. In lattice quantum chromodynamics, DNNs have been used to learn action parameters in regions of parameter -space where PCA fails. Last but not least, -DNNs also found place in the study of quantum, and in scattering theory to learn -$s$-wave scattering length of potentials. +space where PCA fails. + +The applications are not limited to the natural sciences. There is a plethora of applications in essentially all disciplines, from the humanities to life science and medicine. !split ===== Neural network types ===== @@ -471,6 +444,11 @@ plt.show() !ec +!split +===== Setting up a Multi-layer perceptron model ===== + + + !bc pycod from scipy import optimize @@ -828,9 +806,3 @@ net.SGD(training_data,30,10,3,test_data=test_data) !ec -!split -===== Using Tensorflow ===== - -!split -===== Adding deep learning ===== -Convulotional neural networks as well diff --git a/doc/src/NeuralNet/diffeq.tex b/doc/src/NeuralNet/diffeq.tex deleted file mode 100644 index 5897df334..000000000 --- a/doc/src/NeuralNet/diffeq.tex +++ /dev/null @@ -1,1047 +0,0 @@ - -% Default to the notebook output style - - - - -% Inherit from the specified cell style. - - - - - -\documentclass[11pt]{article} - - - - \usepackage[T1]{fontenc} - % Nicer default font (+ math font) than Computer Modern for most use cases - \usepackage{mathpazo} - - % Basic figure setup, for now with no caption control since it's done - % automatically by Pandoc (which extracts ![](path) syntax from Markdown). - \usepackage{graphicx} - % We will generate all images so they have a width \maxwidth. 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-\makeatother - - - % Exact colors from NB - \definecolor{incolor}{rgb}{0.0, 0.0, 0.5} - \definecolor{outcolor}{rgb}{0.545, 0.0, 0.0} - - - - - % Prevent overflowing lines due to hard-to-break entities - \sloppy - % Setup hyperref package - \hypersetup{ - breaklinks=true, % so long urls are correctly broken across lines - colorlinks=true, - urlcolor=urlcolor, - linkcolor=linkcolor, - citecolor=citecolor, - } - % Slightly bigger margins than the latex defaults - - \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} - - - - \begin{document} - - - \maketitle - - - - - - - \hypertarget{example-exponential-decay-in-one-dimension}{% -\section{Example : Exponential decay in one -dimension}\label{example-exponential-decay-in-one-dimension}} - -In this notebook we will see how a neural network performs when solving -the equation - -\[ -\label{eq:ode} -g'(x) = -\gamma g(x) -\] - -where \(g(0) = g_0\) with \(\gamma\) and \(g_0\) being some chosen -values. This equation is an ordinary differential equation since the -function we have to solve for, \(g(x)\), is of one variable. - -In this example, \(\gamma = 2\) and \(g_0 = 10\) but feel free to change -them and see how the neural network performs. - -\hypertarget{trial-solution}{% -\subsection{Trial solution}\label{trial-solution}} - -To begin with, a trial solution \(g_t(t)\) must be chosen. A general -trial solution for ordinary differential equations could be - -\[ -g_t(x, P) = h_1(x) + h_2(x, N(x, P)) -\] - -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. It is assumed that there are no -weights and bias at the input layer, so -\(P = \{ P_{\text{hidden}}, P_{\text{output}} \}\). If there are -\(N_{\text{hidden} }\) neurons in the hidden layer, then -\(P_{\text{hidden}}\) is a \(N_{\text{hidden} } \times 2\) matrix. The -first column in \(P_{\text{hidden} }\) represents the bias for each -neuron in the hidden layer and the second column represents the weigths -for each neuron. 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. Its first -column represents the bias of each neuron and the remaining columns -represents the weights to each neuron. - -It is given that \(g(0) = g_0\). The trial solution must fulfill this -condition to be a proper solution of \eqref{eq:ode}. 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: - -\[ -\label{eq:trial} -g_t(x, P) = g_0 + x \cdot N(x, P) -\] - -\hypertarget{reformulating-the-problem}{% -\subsection{Reformulating the problem}\label{reformulating-the-problem}} - -Often, the role of a neural network is to minimize its parameters with -respect to some given error criteria. This criteria, the cost or loss -function, is a measure of how much error the output of the network has -compared to some given known answers. A reformulation of \eqref{eq:ode} -must therefore be done, such that it describes the problem a neural -network can solve. - -The neural network must find the set of weigths and biases \(P\) such -that the trial solution in \eqref{eq:trial} satisfies \eqref{eq:ode}. -The trial solution has been chosen such that it already solves the -condition \(g(0) = g_0\). What remains, is to find \(P\) such that - -\[ -\label{eq:nnmin} -g_t'(x, P) = - \gamma g_t(x, P) -\] - -is fulfilled as \emph{best as possible}. The left hand and right side of -\eqref{eq:nnmin} must be computed seperately, and then the neural -network will choose which weights and biases in \(P\) makes the sides as -equal as possible. Having two sides of an equation as equal as possible, -means that the absolute or squared difference between the sides must be -as close to zero as small. In this case, the difference squared is an -appropiate measurement of how errorneous the trial solution is with -respect to \(P\) of the neural network. Therefore, the problem our -network must solve, is - -\[ -\min_{P}\Big\{ \big(g_t'(x, P) - ( -\gamma g_t(x, P) \big)^2 \Big\} -\] - -or, in terms of weights and biases for each layer: - -\[ -\min_{P_{\text{hidden} }, \ P_{\text{output} }}\Big\{ \big(g_t'(x, \{ P_{\text{hidden} }, P_{\text{output} }\}) - ( -\gamma g_t(x, \{ P_{\text{hidden} }, P_{\text{output} }\}) \big)^2 \Big\} -\] - -for an input value \(x\). If the neural network evaluates \(g_t(x, P)\) -at more avalues for \(x\),~say \(N\) values \(x_i\) for -\(i = 1, \dots, N\), then the \emph{total} error to minimize is - -\[ \label{eq:min} -\min_{P}\Big\{\sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 \Big\} -\] - -Letting -\(c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2\) -denote the cost function, the minimization problem of which our network -must solve, is - -\[ -\min_{P} c(x, P) -\] - -or in terms of \(P_{\text{hidden} }\) and \(P_{\text{output} }\) - -\[ -\min_{P_{\text{hidden} }, \ P_{\text{output} }} c(x, \{P_{\text{hidden} }, P_{\text{output} }\}) -\] - -\hypertarget{creating-a-simple-deep-neural-net}{% -\subsection{Creating a simple Deep Neural -Net}\label{creating-a-simple-deep-neural-net}} - -The next step is to decide how the neural net \(N(x, P)\) in -\eqref{eq:trial} should be. In this case, the neural network is made -from scratch to understand better how a neural network works, gain more -control over its architecture, and see how Autograd can be used to -simplify the implementation. - -\hypertarget{an-implementation-of-a-neural-network}{% -\subsubsection{An implementation of a Neural -Network}\label{an-implementation-of-a-neural-network}} - -Since a deep neural network (DNN) is a neural network with more than one -hidden layer, we can first look on how to implement a neural network. -Having an implementation of a neural network at hand, an extension of it -into a deep neural network would (hopefully) be painless. - -For simplicity, it is assumed that the input is an array -\(\vec x = (x_1, \dots, x_N)\) with \(N\) elements. It is at these -points the neural network should find \(P\) such that it fulfills -\eqref{eq:min}. - -\hypertarget{feedforward}{% -\paragraph{Feedforward}\label{feedforward}} - -First, a feedforward of the inputs must be done. This means that -\(\vec x\) 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. 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 \(N_{\text{hidden} }\). - -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: - -\[ -\begin{aligned} -z_{i,j}^{\text{hidden}} &= b_i^{\text{hidden}} + w_i^{\text{hidden}}x_j \\ -&= -\begin{pmatrix} -b_i^{\text{hidden}} & w_i^{\text{hidden}} -\end{pmatrix} -\begin{pmatrix} -1 \\ -x_j -\end{pmatrix} -\end{aligned} -\] - -The result after weighting the input at the \(i\)-th hidden neuron can -be written as a vector: - -\[ -\begin{aligned} -\vec{z}_{i}^{\text{hidden}} &= \Big( b_i^{\text{hidden}} + w_i^{\text{hidden}}x_1 , \ b_i^{\text{hidden}} + w_i^{\text{hidden}} x_2, \ \dots \, , \ b_i^{\text{hidden}} + w_i^{\text{hidden}} x_N\Big) \\ -&= -\begin{pmatrix} - b_i^{\text{hidden}} & w_i^{\text{hidden}} -\end{pmatrix} -\begin{pmatrix} -1 & 1 & \dots & 1 \\ -x_1 & x_2 & \dots & x_N -\end{pmatrix} \\ -&= \vec{p}_{i, \text{hidden}}^T X -\end{aligned} -\] - -It is the vector \(\vec{p}_{i, \text{hidden}}^T\) that defines each row -in \(P_{\text{hidden} }\), which contains the weights for the neural -network to minimize according to \eqref{eq:min}. - -After having found \$\vec{z}\_\{i\}\^{}\{\text{hidden}\} \$ for every -neuron \(i\) in the hidden layer, the vector will be sent to an -activation function \(a_i(\vec{z})\). In this example, the sigmoid -function has been used: - -\[ -f(z) = \frac{1}{1 + \exp{(-z)}} -\] - -but feel free to chose any activation function you like. - -The output \(\vec{x}_i^{\text{hidden} }\)from each \(i\)-th hidden -neuron is: - -\[ -\vec{x}_i^{\text{hidden} } = f\big( \vec{z}_{i}^{\text{hidden}} \big) -\] - -The outputs \$\vec{x}\_i\^{}\{\text{hidden} \} \$ are then sent to the -output layer. - -The output layer consist of one neuron in this case, and combines the -output from each of the neurons in the hidden layers. The output layer -combines the results from the hidden layer using some weights \$ -w\_i\^{}\{\text{output}\}\$ and biases \(b_i^{\text{output}}\). In this -case, it is assumes that the number of neurons in the output layer is -one. - -The procedure of weigthing 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. - -\[ -\begin{aligned} -z_{1,j}^{\text{output}} & = -\begin{pmatrix} -b_1^{\text{output}} & \vec{w}_1^{\text{output}} -\end{pmatrix} -\begin{pmatrix} -1 \\ -\vec{x}_j^{\text{hidden}} -\end{pmatrix} -\end{aligned} -\] - -Expressing \(z_{1,j}^{\text{output}}\) as a vector gives the following -procedure of weighting the inputs from the hidden layer: - -\[ -\vec{z}_{1}^{\text{output}} = -\begin{pmatrix} -b_1^{\text{output}} & \vec{w}_1^{\text{output}} -\end{pmatrix} -\begin{pmatrix} -1 & 1 & \dots & 1 \\ -\vec{x}_1^{\text{hidden}} & \vec{x}_2^{\text{hidden}} & \dots & \vec{x}_N^{\text{hidden}} -\end{pmatrix} -\] - -In this case we seek a continous range of values since we are -approximating a function. This means that after computing -\(\vec{z}_{1}^{\text{output}}\) the neural network has finished its -feedforward step, and \(\vec{z}_{1}^{\text{output}}\) is the final -output of the network. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}3}]:} \PY{c+c1}{\PYZsh{} Autograd will be used for later, so the numpy wrapper for Autograd must be imported} - \PY{k+kn}{import} \PY{n+nn}{autograd}\PY{n+nn}{.}\PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np} - \PY{k+kn}{from} \PY{n+nn}{autograd} \PY{k}{import} \PY{n}{grad}\PY{p}{,} \PY{n}{elementwise\PYZus{}grad} - \PY{k+kn}{import} \PY{n+nn}{autograd}\PY{n+nn}{.}\PY{n+nn}{numpy}\PY{n+nn}{.}\PY{n+nn}{random} \PY{k}{as} \PY{n+nn}{npr} - \PY{k+kn}{from} \PY{n+nn}{matplotlib} \PY{k}{import} \PY{n}{pyplot} \PY{k}{as} \PY{n}{plt} - - \PY{k}{def} \PY{n+nf}{sigmoid}\PY{p}{(}\PY{n}{z}\PY{p}{)}\PY{p}{:} - \PY{k}{return} \PY{l+m+mi}{1}\PY{o}{/}\PY{p}{(}\PY{l+m+mi}{1} \PY{o}{+} \PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{z}\PY{p}{)}\PY{p}{)} - - \PY{k}{def} \PY{n+nf}{neural\PYZus{}network}\PY{p}{(}\PY{n}{params}\PY{p}{,} \PY{n}{x}\PY{p}{)}\PY{p}{:} - - \PY{c+c1}{\PYZsh{} Find the weights (including and biases) for the hidden and output layer.} - \PY{c+c1}{\PYZsh{} Assume that params is a list of parameters for each layer. } - \PY{c+c1}{\PYZsh{} The biases are the first element for each array in params, } - \PY{c+c1}{\PYZsh{} and the weights are the remaning elements in each array in params. } - - \PY{n}{w\PYZus{}hidden} \PY{o}{=} \PY{n}{params}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} - \PY{n}{w\PYZus{}output} \PY{o}{=} \PY{n}{params}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} - - \PY{c+c1}{\PYZsh{} Assumes input x being an one\PYZhy{}dimensional array} - \PY{n}{num\PYZus{}values} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{size}\PY{p}{(}\PY{n}{x}\PY{p}{)} - \PY{n}{x} \PY{o}{=} \PY{n}{x}\PY{o}{.}\PY{n}{reshape}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{num\PYZus{}values}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Assume that the input layer does nothing to the input x} - \PY{n}{x\PYZus{}input} \PY{o}{=} \PY{n}{x} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Hidden layer:} - - \PY{c+c1}{\PYZsh{} Add a row of ones to include bias} - \PY{n}{x\PYZus{}input} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{num\PYZus{}values}\PY{p}{)}\PY{p}{)}\PY{p}{,} \PY{n}{x\PYZus{}input} \PY{p}{)}\PY{p}{,} \PY{n}{axis} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{)} - - \PY{n}{z\PYZus{}hidden} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{matmul}\PY{p}{(}\PY{n}{w\PYZus{}hidden}\PY{p}{,} \PY{n}{x\PYZus{}input}\PY{p}{)} - \PY{n}{x\PYZus{}hidden} \PY{o}{=} \PY{n}{sigmoid}\PY{p}{(}\PY{n}{z\PYZus{}hidden}\PY{p}{)} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Output layer:} - - \PY{c+c1}{\PYZsh{} Include bias:} - \PY{n}{x\PYZus{}hidden} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{num\PYZus{}values}\PY{p}{)}\PY{p}{)}\PY{p}{,} \PY{n}{x\PYZus{}hidden} \PY{p}{)}\PY{p}{,} \PY{n}{axis} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{)} - - \PY{n}{z\PYZus{}output} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{matmul}\PY{p}{(}\PY{n}{w\PYZus{}output}\PY{p}{,} \PY{n}{x\PYZus{}hidden}\PY{p}{)} - \PY{n}{x\PYZus{}output} \PY{o}{=} \PY{n}{z\PYZus{}output} - - \PY{k}{return} \PY{n}{x\PYZus{}output} -\end{Verbatim} - - - \hypertarget{backpropagation}{% -\paragraph{Backpropagation}\label{backpropagation}} - -Now that feedforward can be done, the next step is to decide how the -parameters should change such that they minimize the cost function. - -Recall that the chosen cost function for this problem is - -\[ -c(x, P) = \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i, P) \big)^2 -\] - -In order to minimize it, an optimalization method must be chosen. - -Here, gradient descent with a constant step size has been chosen. - -Before looking at the gradient descent method, let us set up the cost -function along with the right ride of the ODE and trial solution. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}4}]:} \PY{c+c1}{\PYZsh{} The trial solution using the deep neural network:} - \PY{k}{def} \PY{n+nf}{g\PYZus{}trial}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{params}\PY{p}{,} \PY{n}{g0} \PY{o}{=} \PY{l+m+mi}{10}\PY{p}{)}\PY{p}{:} - \PY{k}{return} \PY{n}{g0} \PY{o}{+} \PY{n}{x}\PY{o}{*}\PY{n}{neural\PYZus{}network}\PY{p}{(}\PY{n}{params}\PY{p}{,}\PY{n}{x}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} The right side of the ODE:} - \PY{k}{def} \PY{n+nf}{g}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{g\PYZus{}trial}\PY{p}{,} \PY{n}{gamma} \PY{o}{=} \PY{l+m+mi}{2}\PY{p}{)}\PY{p}{:} - \PY{k}{return} \PY{o}{\PYZhy{}}\PY{n}{gamma}\PY{o}{*}\PY{n}{g\PYZus{}trial} - - \PY{c+c1}{\PYZsh{} The cost function:} - \PY{k}{def} \PY{n+nf}{cost\PYZus{}function}\PY{p}{(}\PY{n}{P}\PY{p}{,} \PY{n}{x}\PY{p}{)}\PY{p}{:} - - \PY{c+c1}{\PYZsh{} Evaluate the trial function with the current parameters P} - \PY{n}{g\PYZus{}t} \PY{o}{=} \PY{n}{g\PYZus{}trial}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{P}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Find the derivative w.r.t x of the neural network} - \PY{n}{d\PYZus{}net\PYZus{}out} \PY{o}{=} \PY{n}{elementwise\PYZus{}grad}\PY{p}{(}\PY{n}{neural\PYZus{}network}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{(}\PY{n}{P}\PY{p}{,}\PY{n}{x}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Find the derivative w.r.t x of the trial function} - \PY{n}{d\PYZus{}g\PYZus{}t} \PY{o}{=} \PY{n}{elementwise\PYZus{}grad}\PY{p}{(}\PY{n}{g\PYZus{}trial}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{)}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{P}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} The right side of the ODE } - \PY{n}{func} \PY{o}{=} \PY{n}{g}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{g\PYZus{}t}\PY{p}{)} - - \PY{n}{err\PYZus{}sqr} \PY{o}{=} \PY{p}{(}\PY{n}{d\PYZus{}g\PYZus{}t} \PY{o}{\PYZhy{}} \PY{n}{func}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} - \PY{n}{cost\PYZus{}sum} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{err\PYZus{}sqr}\PY{p}{)} - - \PY{k}{return} \PY{n}{cost\PYZus{}sum} -\end{Verbatim} - - - \hypertarget{gradient-descent}{% -\subparagraph{Gradient Descent}\label{gradient-descent}} - -The idea of the gradient descent algorithm is to update parameters in -direction where the cost function decreases goes to a minimum. - -In general, the update of some parameters \(\vec \omega\) given a cost -function defined by some weights \(\vec \omega\), \(c(x, \vec \omega)\), -goes as follows: - -\[ -\vec \omega_{\text{new} } = \vec \omega - \lambda \nabla_{\vec \omega} c(x, \vec \omega) -\] - -for a number of iterations or until \$ \big\textbar{}\big\textbar{} -\vec \omega\_\{\text{new} \} - -\vec \omega \big\textbar{}\big\textbar{}\$ is smaller than some given -tolerance. - -The value of \(\lambda\) decides how large steps the algorithm must take -in the direction of \$ \nabla\_\{\vec \omega\} c(x, \vec \omega)\$. The -notatation \(\nabla_{\vec \omega}\) denotes the gradient with respect to -the elements in \(\vec \omega\). - -In our case, we have to minimize the cost function \(c(x, P)\) with -respect to the two sets of weights and bisases, that is for the hidden -layer \(P_{\text{hidden} }\) and for the ouput layer -\(P_{\text{output} }\) . - -This means that \(P_{\text{hidden} }\) and \(P_{\text{output} }\) is -updated by - -\[ -\begin{aligned} -P_{\text{hidden},\text{new}} &= P_{\text{hidden}} - \lambda \nabla_{P_{\text{hidden}}} c(x, P) \\ -P_{\text{output},\text{new}} &= P_{\text{output}} - \lambda \nabla_{P_{\text{output}}} c(x, P) -\end{aligned} -\] - -This might look like a cumberstone to set up the correct expression for -finding the gradients. Luckily, Autograd comes to the rescue. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}5}]:} \PY{k}{def} \PY{n+nf}{solve\PYZus{}ode\PYZus{}neural\PYZus{}network}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{num\PYZus{}neurons\PYZus{}hidden}\PY{p}{,} \PY{n}{num\PYZus{}iter}\PY{p}{,} \PY{n}{lmb}\PY{p}{)}\PY{p}{:} - \PY{c+c1}{\PYZsh{}\PYZsh{} Set up initial weigths and biases } - - \PY{c+c1}{\PYZsh{} For the hidden layer} - \PY{n}{p0} \PY{o}{=} \PY{n}{npr}\PY{o}{.}\PY{n}{randn}\PY{p}{(}\PY{n}{num\PYZus{}neurons\PYZus{}hidden}\PY{p}{,} \PY{l+m+mi}{2} \PY{p}{)} - - \PY{c+c1}{\PYZsh{} For the output layer} - \PY{n}{p1} \PY{o}{=} \PY{n}{npr}\PY{o}{.}\PY{n}{randn}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{num\PYZus{}neurons\PYZus{}hidden} \PY{o}{+} \PY{l+m+mi}{1} \PY{p}{)} \PY{c+c1}{\PYZsh{} +1 since bias is included} - - \PY{n}{P} \PY{o}{=} \PY{p}{[}\PY{n}{p0}\PY{p}{,} \PY{n}{p1}\PY{p}{]} - - \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Initial cost: }\PY{l+s+si}{\PYZpc{}g}\PY{l+s+s1}{\PYZsq{}}\PY{o}{\PYZpc{}}\PY{k}{cost\PYZus{}function}(P, x)) - - \PY{c+c1}{\PYZsh{}\PYZsh{} Start finding the optimal weigths using gradient descent} - - \PY{c+c1}{\PYZsh{} Find the Python function that represents the gradient of the cost function} - \PY{c+c1}{\PYZsh{} w.r.t the 0\PYZhy{}th input argument \PYZhy{}\PYZhy{} that is the weights and biases in the hidden and output layer} - \PY{n}{cost\PYZus{}function\PYZus{}grad} \PY{o}{=} \PY{n}{grad}\PY{p}{(}\PY{n}{cost\PYZus{}function}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Let the update be done num\PYZus{}iter times} - \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{num\PYZus{}iter}\PY{p}{)}\PY{p}{:} - \PY{c+c1}{\PYZsh{} Evaluate the gradient at the current weights and biases in P. } - \PY{c+c1}{\PYZsh{} The cost\PYZus{}grad consist now of two arrays; } - \PY{c+c1}{\PYZsh{} one for the gradient w.r.t P\PYZus{}hidden and } - \PY{c+c1}{\PYZsh{} one for the gradient w.r.t P\PYZus{}output} - \PY{n}{cost\PYZus{}grad} \PY{o}{=} \PY{n}{cost\PYZus{}function\PYZus{}grad}\PY{p}{(}\PY{n}{P}\PY{p}{,} \PY{n}{x}\PY{p}{)} - - \PY{n}{P}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{=} \PY{n}{P}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{lmb} \PY{o}{*} \PY{n}{cost\PYZus{}grad}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} - \PY{n}{P}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{P}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{lmb} \PY{o}{*} \PY{n}{cost\PYZus{}grad}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]} - - \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Final cost: }\PY{l+s+si}{\PYZpc{}g}\PY{l+s+s1}{\PYZsq{}}\PY{o}{\PYZpc{}}\PY{k}{cost\PYZus{}function}(P, x)) - - \PY{k}{return} \PY{n}{P} -\end{Verbatim} - - - \hypertarget{an-implementation-of-a-deep-neural-network}{% -\subsubsection{An implementation of a Deep Neural -Network}\label{an-implementation-of-a-deep-neural-network}} - -As previously stated, a Deep Neural Network (DNN) follows the same -concept of a neural network, but having more than one hidden layer. -Suppose that the network has \(N_{\text{hidden}}\) hidden layers where -the \(l\)-th layer has \(N_{\text{hidden}}^{(l)}\) neurons. The input is -still assumed to be an array of size \(1 \times N\). The network must -now try to optimalize its output with respect to the collection of -weigths and biases -\(P = \big\{P_{\text{input} }, \ P_{\text{hidden} }^{(1)}, \ P_{\text{hidden} }^{(2)}, \ \dots , \ P_{\text{hidden} }^{(N_{\text{hidden}})}, \ P_{\text{output} }\big\}\). - -\hypertarget{feedforward}{% -\paragraph{Feedforward}\label{feedforward}} - -The feedforward step is similar to as for the neural netowork, but now -considering more than one hidden layer. - -The \(i\)-th neuron at layer \(l\) recieves the result -\(\vec{x}_j^{(l-1),\text{hidden} }\) from the \(j\)-th neuron at layer -\(l-1\). The \(i\)-th neuron at layer \(l\) weights all of the elements -in \(\vec{x}_j^{(l-1),\text{hidden} }\) with a weight vector -\(\vec w_{i,j}^{(l), \ \text{hidden} }\) with as many weigths as there -are elements in\(\vec{x}_j^{(l-1),\text{hidden} }\), and adds a bias -\(b_i^{(l), \ \text{hidden} }\): - -\[ -\begin{aligned} -z_{i,j}^{(l),\ \text{hidden}} &= b_i^{(l), \ \text{hidden}} + \big(\vec{w}_{i}^{(l), \ \text{hidden}}\big)^T\vec{x}_j^{(l-1),\text{hidden} } \\ -&= -\begin{pmatrix} -b_i^{(l), \ \text{hidden}} & \big(\vec{w}_{i}^{(l), \ \text{hidden}}\big)^T -\end{pmatrix} -\begin{pmatrix} -1 \\ -\vec{x}_j^{(l-1),\text{hidden} } -\end{pmatrix} -\end{aligned} -\] - -The output from the \(i\)-th neuron at the hidden layer \(l\) becomes a -vector \(\vec{z}_{i}^{(l),\ \text{hidden}}\): - -\[ -\begin{aligned} -\vec{z}_{i}^{(l),\ \text{hidden}} &= \Big( b_i^{(l), \ \text{hidden}} + \big(\vec{w}_{i}^{(l), \ \text{hidden}}\big)^T\vec{x}_1^{(l-1),\text{hidden} }, \ \dots \ , \ b_i^{(l), \ \text{hidden}} + \big(\vec{w}_{i}^{(l), \ \text{hidden}}\big)^T\vec{x}_{N_{hidden}^{(l-1)}}^{(l-1),\text{hidden} } \Big) \\ -&= -\begin{pmatrix} -b_i^{(l), \ \text{hidden}} & \big(\vec{w}_{i}^{(l), \ \text{hidden}}\big)^T -\end{pmatrix} -\begin{pmatrix} -1 & 1 & \dots & 1 \\ -\vec{x}_{1}^{(l-1),\text{hidden} } & \vec{x}_{2}^{(l-1),\text{hidden} } & \dots & \vec{x}_{N_{hidden}^{(l-1)}}^{(l-1),\text{hidden} } -\end{pmatrix} -\end{aligned} -\] - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}237}]:} \PY{k}{def} \PY{n+nf}{deep\PYZus{}neural\PYZus{}network}\PY{p}{(}\PY{n}{deep\PYZus{}params}\PY{p}{,} \PY{n}{x}\PY{p}{)}\PY{p}{:} - \PY{c+c1}{\PYZsh{} N\PYZus{}hidden is the number of hidden layers } - \PY{n}{N\PYZus{}hidden} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{size}\PY{p}{(}\PY{n}{deep\PYZus{}params}\PY{p}{)} \PY{o}{\PYZhy{}} \PY{l+m+mi}{1} \PY{c+c1}{\PYZsh{} \PYZhy{}1 since params consist of parameters to all the hidden layers AND the output layer} - - \PY{c+c1}{\PYZsh{} Assumes input x being an one\PYZhy{}dimensional array} - \PY{n}{num\PYZus{}values} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{size}\PY{p}{(}\PY{n}{x}\PY{p}{)} - \PY{n}{x} \PY{o}{=} \PY{n}{x}\PY{o}{.}\PY{n}{reshape}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{num\PYZus{}values}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Assume that the input layer does nothing to the input x} - \PY{n}{x\PYZus{}input} \PY{o}{=} \PY{n}{x} - - \PY{c+c1}{\PYZsh{} Due to multiple hidden layers, define a variable referencing to the} - \PY{c+c1}{\PYZsh{} output of the previous layer:} - \PY{n}{x\PYZus{}prev} \PY{o}{=} \PY{n}{x\PYZus{}input} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Hidden layers:} - - \PY{k}{for} \PY{n}{l} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{N\PYZus{}hidden}\PY{p}{)}\PY{p}{:} - \PY{c+c1}{\PYZsh{} From the list of parameters P; find the correct weigths and bias for this layer} - \PY{n}{w\PYZus{}hidden} \PY{o}{=} \PY{n}{deep\PYZus{}params}\PY{p}{[}\PY{n}{l}\PY{p}{]} - - \PY{c+c1}{\PYZsh{} Add a row of ones to include bias} - \PY{n}{x\PYZus{}prev} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{num\PYZus{}values}\PY{p}{)}\PY{p}{)}\PY{p}{,} \PY{n}{x\PYZus{}prev} \PY{p}{)}\PY{p}{,} \PY{n}{axis} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{)} - - \PY{n}{z\PYZus{}hidden} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{matmul}\PY{p}{(}\PY{n}{w\PYZus{}hidden}\PY{p}{,} \PY{n}{x\PYZus{}prev}\PY{p}{)} - \PY{n}{x\PYZus{}hidden} \PY{o}{=} \PY{n}{sigmoid}\PY{p}{(}\PY{n}{z\PYZus{}hidden}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Update x\PYZus{}prev such that next layer can use the output from this layer} - \PY{n}{x\PYZus{}prev} \PY{o}{=} \PY{n}{x\PYZus{}hidden} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Output layer:} - - \PY{c+c1}{\PYZsh{} Get the weights and bias for this layer} - \PY{n}{w\PYZus{}output} \PY{o}{=} \PY{n}{deep\PYZus{}params}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} - - \PY{c+c1}{\PYZsh{} Include bias:} - \PY{n}{x\PYZus{}prev} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{concatenate}\PY{p}{(}\PY{p}{(}\PY{n}{np}\PY{o}{.}\PY{n}{ones}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{num\PYZus{}values}\PY{p}{)}\PY{p}{)}\PY{p}{,} \PY{n}{x\PYZus{}prev}\PY{p}{)}\PY{p}{,} \PY{n}{axis} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{)} - - \PY{n}{z\PYZus{}output} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{matmul}\PY{p}{(}\PY{n}{w\PYZus{}output}\PY{p}{,} \PY{n}{x\PYZus{}prev}\PY{p}{)} - \PY{n}{x\PYZus{}output} \PY{o}{=} \PY{n}{z\PYZus{}output} - - \PY{k}{return} \PY{n}{x\PYZus{}output} -\end{Verbatim} - - - \hypertarget{backpropagation}{% -\paragraph{Backpropagation}\label{backpropagation}} - -This step is very similar for the neural network. The idea in this step -is the same as for the neural network, but with more parameters to -update for. Again there is no need for computing the gradients -analytically since Autograd does the work for us. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}215}]:} \PY{c+c1}{\PYZsh{} The trial solution using the deep neural network:} - \PY{k}{def} \PY{n+nf}{g\PYZus{}trial\PYZus{}deep}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{params}\PY{p}{,} \PY{n}{g0} \PY{o}{=} \PY{l+m+mi}{10}\PY{p}{)}\PY{p}{:} - \PY{k}{return} \PY{n}{g0} \PY{o}{+} \PY{n}{x}\PY{o}{*}\PY{n}{deep\PYZus{}neural\PYZus{}network}\PY{p}{(}\PY{n}{params}\PY{p}{,}\PY{n}{x}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} The same cost function as for the neural network, but calls deep\PYZus{}neural\PYZus{}network instead.} - \PY{k}{def} \PY{n+nf}{cost\PYZus{}function\PYZus{}deep}\PY{p}{(}\PY{n}{P}\PY{p}{,} \PY{n}{x}\PY{p}{)}\PY{p}{:} - - \PY{c+c1}{\PYZsh{} Evaluate the trial function with the current parameters P} - \PY{n}{g\PYZus{}t} \PY{o}{=} \PY{n}{g\PYZus{}trial\PYZus{}deep}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{P}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Find the derivative w.r.t x of the neural network} - \PY{n}{d\PYZus{}net\PYZus{}out} \PY{o}{=} \PY{n}{elementwise\PYZus{}grad}\PY{p}{(}\PY{n}{deep\PYZus{}neural\PYZus{}network}\PY{p}{,}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{(}\PY{n}{P}\PY{p}{,}\PY{n}{x}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Find the derivative w.r.t x of the trial function} - \PY{n}{d\PYZus{}g\PYZus{}t} \PY{o}{=} \PY{n}{elementwise\PYZus{}grad}\PY{p}{(}\PY{n}{g\PYZus{}trial\PYZus{}deep}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{)}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{P}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} The right side of the ODE } - \PY{n}{func} \PY{o}{=} \PY{n}{g}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{g\PYZus{}t}\PY{p}{)} - - \PY{n}{err\PYZus{}sqr} \PY{o}{=} \PY{p}{(}\PY{n}{d\PYZus{}g\PYZus{}t} \PY{o}{\PYZhy{}} \PY{n}{func}\PY{p}{)}\PY{o}{*}\PY{o}{*}\PY{l+m+mi}{2} - \PY{n}{cost\PYZus{}sum} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{sum}\PY{p}{(}\PY{n}{err\PYZus{}sqr}\PY{p}{)} - - \PY{k}{return} \PY{n}{cost\PYZus{}sum} - - \PY{k}{def} \PY{n+nf}{solve\PYZus{}ode\PYZus{}deep\PYZus{}neural\PYZus{}network}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{num\PYZus{}neurons}\PY{p}{,} \PY{n}{num\PYZus{}iter}\PY{p}{,} \PY{n}{lmb}\PY{p}{)}\PY{p}{:} - \PY{c+c1}{\PYZsh{} num\PYZus{}hidden\PYZus{}neurons is now a list of number of neurons within each hidden layer} - - \PY{c+c1}{\PYZsh{} Find the number of hidden layers:} - \PY{n}{N\PYZus{}hidden} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{size}\PY{p}{(}\PY{n}{num\PYZus{}neurons}\PY{p}{)} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Set up initial weigths and biases } - - \PY{c+c1}{\PYZsh{} Initialize the list of parameters:} - \PY{n}{P} \PY{o}{=} \PY{p}{[}\PY{k+kc}{None}\PY{p}{]}\PY{o}{*}\PY{p}{(}\PY{n}{N\PYZus{}hidden} \PY{o}{+} \PY{l+m+mi}{1}\PY{p}{)} \PY{c+c1}{\PYZsh{} + 1 to include the output layer} - - \PY{n}{P}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]} \PY{o}{=} \PY{n}{npr}\PY{o}{.}\PY{n}{randn}\PY{p}{(}\PY{n}{num\PYZus{}neurons}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{p}{,} \PY{l+m+mi}{2} \PY{p}{)} - \PY{k}{for} \PY{n}{l} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{n}{N\PYZus{}hidden}\PY{p}{)}\PY{p}{:} - \PY{n}{P}\PY{p}{[}\PY{n}{l}\PY{p}{]} \PY{o}{=} \PY{n}{npr}\PY{o}{.}\PY{n}{randn}\PY{p}{(}\PY{n}{num\PYZus{}neurons}\PY{p}{[}\PY{n}{l}\PY{p}{]}\PY{p}{,} \PY{n}{num\PYZus{}neurons}\PY{p}{[}\PY{n}{l}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{+} \PY{l+m+mi}{1}\PY{p}{)} \PY{c+c1}{\PYZsh{} +1 to include bias } - - \PY{c+c1}{\PYZsh{} For the output layer} - \PY{n}{P}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{=} \PY{n}{npr}\PY{o}{.}\PY{n}{randn}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,} \PY{n}{num\PYZus{}neurons}\PY{p}{[}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]} \PY{o}{+} \PY{l+m+mi}{1} \PY{p}{)} \PY{c+c1}{\PYZsh{} +1 since bias is included} - - \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Initial cost: }\PY{l+s+si}{\PYZpc{}g}\PY{l+s+s1}{\PYZsq{}}\PY{o}{\PYZpc{}}\PY{k}{cost\PYZus{}function\PYZus{}deep}(P, x)) - - \PY{c+c1}{\PYZsh{}\PYZsh{} Start finding the optimal weigths using gradient descent} - - \PY{c+c1}{\PYZsh{} Find the Python function that represents the gradient of the cost function} - \PY{c+c1}{\PYZsh{} w.r.t the 0\PYZhy{}th input argument \PYZhy{}\PYZhy{} that is the weights and biases in the hidden and output layer} - \PY{n}{cost\PYZus{}function\PYZus{}deep\PYZus{}grad} \PY{o}{=} \PY{n}{grad}\PY{p}{(}\PY{n}{cost\PYZus{}function\PYZus{}deep}\PY{p}{,}\PY{l+m+mi}{0}\PY{p}{)} - - \PY{c+c1}{\PYZsh{} Let the update be done num\PYZus{}iter times} - \PY{k}{for} \PY{n}{i} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{num\PYZus{}iter}\PY{p}{)}\PY{p}{:} - \PY{c+c1}{\PYZsh{} Evaluate the gradient at the current weights and biases in P. } - \PY{c+c1}{\PYZsh{} The cost\PYZus{}grad consist now of N\PYZus{}hidden + 1 arrays; the gradient w.r.t the weights and biases} - \PY{c+c1}{\PYZsh{} in the hidden layers and output layers evaluated at x.} - \PY{n}{cost\PYZus{}deep\PYZus{}grad} \PY{o}{=} \PY{n}{cost\PYZus{}function\PYZus{}deep\PYZus{}grad}\PY{p}{(}\PY{n}{P}\PY{p}{,} \PY{n}{x}\PY{p}{)} - - \PY{k}{for} \PY{n}{l} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{N\PYZus{}hidden}\PY{o}{+}\PY{l+m+mi}{1}\PY{p}{)}\PY{p}{:} - \PY{n}{P}\PY{p}{[}\PY{n}{l}\PY{p}{]} \PY{o}{=} \PY{n}{P}\PY{p}{[}\PY{n}{l}\PY{p}{]} \PY{o}{\PYZhy{}} \PY{n}{lmb} \PY{o}{*} \PY{n}{cost\PYZus{}deep\PYZus{}grad}\PY{p}{[}\PY{n}{l}\PY{p}{]} - - \PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Final cost: }\PY{l+s+si}{\PYZpc{}g}\PY{l+s+s1}{\PYZsq{}}\PY{o}{\PYZpc{}}\PY{k}{cost\PYZus{}function\PYZus{}deep}(P, x)) - - \PY{k}{return} \PY{n}{P} -\end{Verbatim} - - - \hypertarget{solving-the-ode}{% -\subsection{Solving the ODE}\label{solving-the-ode}} - -Finally, having set up the networks we are ready to use them to solve -the ODE problem. - -If possible, it is always useful to have an analytical solution at hand -to test if the implementations gives reasonable results. - -As a recap, the equation to solve is - -\[ -g'(x) = -\gamma g(x) -\] - -where \(g(0) = g_0\) with \(\gamma\) and \(g_0\) being some chosen -values. - -Solving this analytically yields - -\[ -g(x) = g_0\exp(-\gamma x) -\] - -By making the analytical solution availible in our program, it is -possible to check the persomance of our neural networks. - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}196}]:} \PY{k}{def} \PY{n+nf}{g\PYZus{}analytic}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{gamma} \PY{o}{=} \PY{l+m+mi}{2}\PY{p}{,} \PY{n}{g0} \PY{o}{=} \PY{l+m+mi}{10}\PY{p}{)}\PY{p}{:} - \PY{k}{return} \PY{n}{g0}\PY{o}{*}\PY{n}{np}\PY{o}{.}\PY{n}{exp}\PY{p}{(}\PY{o}{\PYZhy{}}\PY{n}{gamma}\PY{o}{*}\PY{n}{x}\PY{p}{)} -\end{Verbatim} - - - \hypertarget{using-neural-network}{% -\subsubsection{Using neural network}\label{using-neural-network}} - -The code below solves the ODE using a neural network. The number of -values for the input \(\vec x\) is 10, number of hidden neurons in the -hidden layer being 10 and th step size used in gradien descent -\(\lambda = 0.001\). The program updates the weights and biases in the -network \emph{num\_iter} times. Finally, it plots the results from using -the neural network along with the analytical solution. Feel free to -experiment with different values and see how the performance of the -network is! - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor}6}]:} \PY{n}{npr}\PY{o}{.}\PY{n}{seed}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{)} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Decide the vales of arguments to the function to solve} - \PY{n}{N} \PY{o}{=} \PY{l+m+mi}{10} - \PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{n}{N}\PY{p}{)} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Set up the initial parameters} - \PY{n}{num\PYZus{}hidden\PYZus{}neurons} \PY{o}{=} \PY{l+m+mi}{10} - \PY{n}{num\PYZus{}iter} \PY{o}{=} \PY{l+m+mi}{10000} - \PY{n}{lmb} \PY{o}{=} \PY{l+m+mf}{0.001} - - \PY{n}{P} \PY{o}{=} \PY{n}{solve\PYZus{}ode\PYZus{}neural\PYZus{}network}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{num\PYZus{}hidden\PYZus{}neurons}\PY{p}{,} \PY{n}{num\PYZus{}iter}\PY{p}{,} \PY{n}{lmb}\PY{p}{)} - - \PY{n}{res} \PY{o}{=} \PY{n}{g\PYZus{}trial}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{P}\PY{p}{)} - \PY{n}{res\PYZus{}analytical} \PY{o}{=} \PY{n}{g\PYZus{}analytic}\PY{p}{(}\PY{n}{x}\PY{p}{)} - - \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{)} - - \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Performance of neural network solving an ODE compared to the analytical solution}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{res\PYZus{}analytical}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{res}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,}\PY{p}{:}\PY{p}{]}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{analytical}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{nn}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{xlabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{x}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{g(x)}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} -\end{Verbatim} - - - \begin{Verbatim}[commandchars=\\\{\}] -Initial cost: 3670.1 -Final cost: 0.0510011 - - \end{Verbatim} - - \begin{Verbatim}[commandchars=\\\{\}] - - --------------------------------------------------------------------------- - - NameError Traceback (most recent call last) - - in () - 13 - 14 res = g\_trial(x,P) - ---> 15 res\_analytical = g\_analytic(x) - 16 - 17 plt.figure(figsize=(10,10)) - - - NameError: name 'g\_analytic' is not defined - - \end{Verbatim} - - \hypertarget{using-a-deep-neural-network}{% -\subsubsection{Using a deep neural -network}\label{using-a-deep-neural-network}} - - \begin{Verbatim}[commandchars=\\\{\}] -{\color{incolor}In [{\color{incolor} }]:} \PY{n}{npr}\PY{o}{.}\PY{n}{seed}\PY{p}{(}\PY{l+m+mi}{15}\PY{p}{)} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Decide the vales of arguments to the function to solve} - \PY{n}{N} \PY{o}{=} \PY{l+m+mi}{10} - \PY{n}{x} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{linspace}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,} \PY{l+m+mi}{1}\PY{p}{,} \PY{n}{N}\PY{p}{)} - - \PY{c+c1}{\PYZsh{}\PYZsh{} Set up the initial parameters} - \PY{n}{num\PYZus{}hidden\PYZus{}neurons} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{array}\PY{p}{(}\PY{p}{[}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{]}\PY{p}{)} - \PY{n}{num\PYZus{}iter} \PY{o}{=} \PY{l+m+mi}{10000} - \PY{n}{lmb} \PY{o}{=} \PY{l+m+mf}{0.001} - - \PY{n}{P} \PY{o}{=} \PY{n}{solve\PYZus{}ode\PYZus{}deep\PYZus{}neural\PYZus{}network}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{num\PYZus{}hidden\PYZus{}neurons}\PY{p}{,} \PY{n}{num\PYZus{}iter}\PY{p}{,} \PY{n}{lmb}\PY{p}{)} - - \PY{n}{res} \PY{o}{=} \PY{n}{g\PYZus{}trial\PYZus{}deep}\PY{p}{(}\PY{n}{x}\PY{p}{,}\PY{n}{P}\PY{p}{)} - \PY{n}{res\PYZus{}analytical} \PY{o}{=} \PY{n}{g\PYZus{}analytic}\PY{p}{(}\PY{n}{x}\PY{p}{)} - - \PY{n}{plt}\PY{o}{.}\PY{n}{figure}\PY{p}{(}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{10}\PY{p}{)}\PY{p}{)} - - \PY{n}{plt}\PY{o}{.}\PY{n}{title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Performance of a deep neural network solving an ODE compared to the analytical solution}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{res\PYZus{}analytical}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{x}\PY{p}{,} \PY{n}{res}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{,}\PY{p}{:}\PY{p}{]}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{legend}\PY{p}{(}\PY{p}{[}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{analytical}\PY{l+s+s1}{\PYZsq{}}\PY{p}{,}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{dnn}\PY{l+s+s1}{\PYZsq{}}\PY{p}{]}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{ylabel}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{g(x)}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)} - \PY{n}{plt}\PY{o}{.}\PY{n}{show}\PY{p}{(}\PY{p}{)} -\end{Verbatim} - - - \hypertarget{wrapping-it-up}{% -\subsection{Wrapping it up}\label{wrapping-it-up}} - -By rewriting the ODE as a minimization problem, it was possible to solve -equation using either a neural network (one hidden layer) or a deep -neural network (more than one hidden layers). How well the network -performed is measured by a specified cost function, which is the -function the network tries to minimize. Using a trial solution which -satisfies the additional condition and being defined by using the output -from the network in some way, the minimization problem could be -explicitly defined for out network to solve. The proposed solution from -the network is then the trial solution with parameters, that is weights -and biases within each layer in the network, such that the solution -minimizes the cost function. - - - % Add a bibliography block to the postdoc - - - - \end{document}