We end our discussion on neural networks with a discussion on how to solve differential equations. Here we focus first on the classical exponential decay in one dimension. Thereafter we switch to the Poisson equation in one dimension.
The aim is to see if we can use a neural network to solve $$ \begin{equation} \tag{16} g'(x) = -\gamma g(x) \end{equation} $$
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.
Here we set \( \gamma = 2 \) and \( g_0 = 10 \) but feel free to change them and see how the neural network performs.