Differentiable Turbulence II
Varun Shankar Romit Maulik Venkatasubramanian Viswanathan
Differentiable fluid simulators are increasingly demonstrating value as
useful tools for developing data-driven models in computational fluid dynamics
(CFD). Differentiable turbulence, or the end-to-end training of machine
learning (ML) models embedded in CFD solution algorithms, captures both the
generalization power and limited upfront cost of physics-based simulations, and
the flexibility and automated training of deep learning methods. We develop a
framework for integrating deep learning models into a generic finite element
numerical scheme for solving the Navier-Stokes equations, applying the
technique to learn a sub-grid scale closure using a multi-scale graph neural
network. We demonstrate the method on several realizations of flow over a
backwards-facing step, testing on both unseen Reynolds numbers and new
geometry. We show that the learned closure can achieve accuracy comparable to
traditional large eddy simulation on a finer grid that amounts to an equivalent
speedup of 10x. As the desire and need for cheaper CFD simulations grows, we
see hybrid physics-ML methods as a path forward to be exploited in the near
future.