Towards learning Lattice Boltzmann collision operators

TL;DR

This paper investigates learning collision operators for the Lattice Boltzmann Method using deep learning, demonstrating that embedding physical properties significantly improves accuracy in reproducing fluid flow dynamics.

Contribution

It introduces a neural network approach to learn LBM collision operators and shows that incorporating physical laws enhances model accuracy substantially.

Findings

Vanilla neural networks have limited accuracy.

Embedding physical properties improves accuracy by orders of magnitude.

The method accurately reproduces fluid flow dynamics over time.

Abstract

In this work we explore the possibility of learning from data collision operators for the Lattice Boltzmann Method using a deep learning approach. We compare a hierarchy of designs of the neural network (NN) collision operator and evaluate the performance of the resulting LBM method in reproducing time dynamics of several canonical flows. In the current study, as a first attempt to address the learning problem, the data was generated by a single relaxation time BGK operator. We demonstrate that vanilla NN architecture has very limited accuracy. On the other hand, by embedding physical properties, such as conservation laws and symmetries, it is possible to dramatically increase the accuracy by several orders of magnitude and correctly reproduce the short and long time dynamics of standard fluid flows.