Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence

Abstract

We demonstrate an approach to enforce mass conservation constraints for three-dimensional incompressible turbulence inside the convolutional neural network architecture. Our method shows increased interpretability and adheres to periodic boundary conditions, while showing high accuracy. This approach is generic for differential constraints L of the form L(V) = G, and can be extended to different applications and neural network architectures.