Analysis of Physics informed Neural Networks applied to the 2D Acoustic Wave Equation in Complex Media

Abstract

In this thesis we have analysed the behaviour of a physics informed neural network and it’s competence in predicting a wave in a non-homogeneous medium. During this project we have used a fully connected network with labelled input data of a 2D acoustic wave. On top of this we used a special loss function that calculated whether the output of the network satisfies the wave equation. Our experiment consisted of the tuning of the hyper parameters, analysing the optimal choice of activation function and the optimisation of the input data and improving the loss function. During this project the unpredictable nature of machine learning has become very clear. We have experimented with several activation functions and have found that the optimal choice of activation function depends on how long you are willing to train the network, as the development of the loss function differs immensely between activation functions. When we looked at the optimal scaling of the input values we find that a non-trivial scaling seems to work better than for example, normalisation of these values. Furthermore we have tried to improve the sampling of the points we use to calculate whether the prediction of the neural network satisfies the wave equation and got interesting results. When we implement all op- timisation techniques, we find that the neural network is extremely capable of predicting the wave’s behaviour in a high contrast media within the time frames of the input data. Prediction outside of this time frame does work but the results do deteriorate especially in the positive time direction. Predicting in the negative time direction yield slightly better results.