The Universal Approximation Theorem states that a neural network can approximate any function at a single hidden layer along with one input and output layer to any given precision.

An Introduction to Neural Network Methods for Differential Equations, by Yadav and Kumar.

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next, by Cuomo et al

The lectures on differential equations were developed by Kristine Baluka Hein, now PhD student at IFI. A great thanks to Kristine.