A Short Note on Physics-Guided GAN to Learn Physical Models without Gradients

Abstract

This study briefly describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. The proposed method does not need the gradients of the physical equations, although the conventional physics-informed models need the gradients. DNNs are widely used to predict phenomena in physics and mechanics. One of the issues with DNNs is that their output does not always satisfy physical equations. One approach to consider with physical equations is adding a residual of the equations into the loss function; this is called physics-informed neural network (PINN). One feature of PINNs is that the physical equations and corresponding residuals must be implemented as part of a neural network model. In addition, the residual does not always converge to a small value. The proposed model is a physics-guided generative adversarial network (PG-GAN) that uses a GAN architecture, in which physical equations are used to judge whether the neural network’s output is consistent with physics. The proposed method was applied to a simple problem to assess its potential usability.