Physics-Informed Generative Learning to Emulate Unresolved Physics in Climate Models

Simulating Earth's climate often involves solving nonlinear coupled PDEs with multi-scale physics that cannot be fully resolved and requires parameterizations for sub-grid scale phenomena. Therefore, reliable and accurate models to parameterize unresolved and under-resolved physics, such as atmospheric convection, remain an important requirement for simulating climate systems. Recently, Machine Learning has proven to be successful in many data-driven 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 examples from hi-fidelity simulations or experimental data as training data. We present a physics-informed generative adversarial network, i.e., GANs that incorporate constraints of both conservation laws and certain statistical properties obtained from the training data (hi-fidelity simulations of Rayleigh-Benard convection). By training both standard GANs and physics-informed GANs as emulators of Rayleigh-Benard convection, we show that the physics-informed GAN is more robust and better captures high-order statistics. This work has great potential as an alternative to the explicit modeling of closures for unresolved physics, which account for a major source of uncertainty when simulating Earth’s climate.