Differentiable physics-enabled closure modeling for Burgers' turbulence

TL;DR

This paper introduces a differentiable physics-based machine learning approach for turbulence modeling in Burgers' equation, demonstrating improved accuracy, efficiency, and interpretability over existing methods.

Contribution

It develops physics-informed neural closure models for Burgers' turbulence, integrating known physics to enhance data efficiency and generalization.

Findings

Physics-informed models outperform baselines in accuracy.

Models are highly data-efficient and generalizable.

Adding physics structure improves interpretability.

Abstract

Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers' turbulence. We consider the 1D Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.