A PHYSICS-INFORMED NEURAL OPERATOR FOR THE SIMULATION OF SURFACE WAVES

Abstract

We develop and implement a Neural Operator (NOp) to predict the evolution of waves on the surface of water. The NOp uses a Graph Neural Network (GNN) to connect randomly sampled points on the water surface and exchange information between them to make the prediction. Our main contribution is adding physical knowledge to the implementation, which allows the model to be to be more general and able to be used in domains of different geometries with no retraining. Our implementation also takes advantage of the fact that the governing equations are independent of rotation and translation to make training easier. In this work, the model is trained with data from a single domain with fixed dimensions and evaluated in domains of different dimensions with little impact to performance. We believe this technique could be extended to more complex problems, such as simulating water currents in environments with more complicated geometries. It may also be possible to use encoding models that are aware of temporal evolution to predict a full time series instead of just a snapshot.