Finite-Element-Based Physics-Informed Convolutional Neural Networks

Physics informed neural networks have become very popular as a technique for solving physics-derived partial differential equations. However, many PINN techniques do not allow for variation in geometry and parameters after training. Relatedly, PINNs are usually constructed with fully-connected NNs, making them costly to train. In this talk, we present a PINN methodology which leverages the finite element method to enable variation in geometry and parameters within a convolutional NN architecture. The heart of the method is a new type of convolutional operation called stencil convolution which utilizes the finite element inverse isoparametric map. We demonstrate the method with applications to deformations of linear elastic solids.