Embedding Hard Physical Constraints in Neural Network Coarse-Graining of 3D Turbulence

TL;DR

This paper introduces a neural network framework that embeds physical constraints of incompressible fluids directly into the model, significantly improving mass conservation in 3D turbulence simulations.

Contribution

It presents a novel physics-embedded neural network approach for coarse-graining turbulent flows, integrating physical laws into deep learning models for better accuracy.

Findings

Enhanced local mass conservation in turbulence modeling

Maintained performance metrics while enforcing physical constraints

Applicable to 3D fully-developed turbulence simulations

Abstract

In the recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of PDEs is enforcing physical constraints and boundary conditions. In this work, we propose a general framework to directly embed the notion of an incompressible fluid into Convolutional Neural Networks, and apply this to coarse-graining of turbulent flow. These physics-embedded neural networks leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. We demonstrate results on three-dimensional fully-developed turbulence, showing that this technique drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.