Physics-Informed Generative Learning to Predict Unresolved Physics in Complex Systems

Simulating complex physical systems often involves solving partial differential equations (PDEs) with closures due to the presence of multi-scale physics. Although the advancement of high-performance computing has made resolving small-scale physics possible, such simulations are still very expensive. Therefore, reliable and accurate models for the unresolved physics remain an important requirement for many complex systems, e.g., turbulent flows. Recently, machine learning techniques have been explored in many data-driven physical modeling problems, and several researchers adopted generative adversarial networks (GANs) to generate solutions of PDEs governed complex systems by training on some existing simulation results from these PDEs. We present a physics-informed GAN by enforcing constraints of both conservation laws and certain statistical properties from the training data. We show that physics-informed GAN is more robust and better captures high-order statistics. These results suggest that physics-informed GANs may be an attractive alternative to the explicit modeling of closures for unresolved physics, which account for a major source of uncertainty when simulating complex systems, e.g., turbulent flows and Earth’s climate.