Embedding Hard Physical Constraints in Convolutional Neural Networks for 3D Turbulence

Arvind T. Mohan, Nicholas Lubbers, Daniel Livescu, Michael Chertkov

Keywords: Physics Conservation Laws, Numerical Methods, Convolutional Neural Networks

TL;DR: We exploit the connection between CNNs and traditional finite difference/volume numerical methods to explicitly enforce mass conservation laws in fluids as a strong inductive bias without relying on loss function penalties.

Abstract: Deep learning approaches have shown much promise for physical sciences, especially in dimensionality reduction and compression of large datasets. A major issue in deep learning of large-scale phenomena, like fluid turbulence, is the lack of physical guarantees. In this work, we propose a general framework to directly embed the notion of incompressible fluids into Convolutional Neural Networks, for coarse-graining of turbulence. These \textbf{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 3D fully-developed turbulence, showing that the \textit{physics-aware inductive bias} drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.