Physics-informed neural networks with non-differentiable loss

Abstract

Physics-informed Neural Networks (PINN) are special neural networks that are designed for scientific computing tasks. Recent research has found its promising capability to integrate any given law of physics in different forms including general nonlinear partial differentiable equations. It has shown great potential to function as a data-efficient universal function approximator that is able to encode any underlying physical laws as prior information. However, just like other ordinary neural networks, the usage of such knowledge still relies on the optimization of neural networks which implies that a differentiable loss function is indispensable. Yet sometimes human knowledge contradict such requirement and knowledge, such as qualitative conclusions, can not be constructed into PINN directly. After a delicate literature review, the surrogate model was chosen as a better fit to substitute the original loss function, which can reconstruct a continuous and differentiable function from samples from the original function. We then propose the PINN with surrogate loss (SL-PINN). It greatly boosts the performance when integrating human knowledge into the neural network