Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations

Jaideep Pathak (NERSC)

Abstract

Simulation of turbulent flows at high Reynolds number is a computationally challenging task relevant to a large number of engineering and scientific applications in diverse fields such as climate science, aerodynamics, and combustion. Turbulent flows are typically modeled by the Navier-Stokes equations. Direct Numerical Simulation (DNS) of the Navier-Stokes equations with sufficient numerical resolution to capture all the relevant scales of the turbulent motions can be prohibitively expensive. Simulation at lower-resolution on a coarse-grid introduces significant errors. We introduce a machine learning (ML) technique based on a deep neural network architecture that corrects the numerical errors induced by a coarse-grid simulation of turbulent flows at high-Reynolds numbers, while simultaneously recovering an estimate of the high-resolution fields. Our proposed simulation strategy is a hybrid ML-PDE solver that is capable of obtaining a meaningful high-resolution solution trajectory while solving the system PDE at a lower resolution. The approach has the potential to dramatically reduce the expense of turbulent flow simulations. As a proof-of-concept, we demonstrate our ML-PDE strategy on a two-dimensional Rayleigh-Bénard Convection (RBC) problem.

Bio

Jaideep Pathak is a NESAP for Learning Postdoctoral Fellow at NERSC, Lawrence Berkeley National Laboratory working on incorporating machine learning learning techniques for problems in computational fluid dynamics. He joined NERSC after receiving his PhD from the University of Maryland, College Park in December 2019. His primary interests are in developing machine learning techniques for improving simulations in diverse fields such as weather forecasting and climate modeling, fluid turbulence, and combustion.