Physics-Informed Generative Adversarial Networks by Incorporating Conservation Laws

Recently, machine learning techniques have proven to be successful in many data-driven physical modeling tasks, including in mimicking distributions of processes in complex systems using a flavor of deep neural networks called generative adversarial networks (GANs). GANs have also been designed to generate solutions of PDEs governing complex systems without having to numerically solve these PDEs, by using existing high-fidelity simulations or experimental data as training data. In this work, we present a physics-informed GAN by enforcing constraints of conservation laws to improve the quality of the generated solutions of GANs. We show that this physics-informed GAN generates more realistic solutions of potential flows compared to traditional GANs without any physical constraints. These results suggest that the physics-informed GAN is more suitable for the task of physical modeling and has great potential in many areas where directly simulating the physics is usually expansive, e.g., turbulence.