Toward learning Lattice Boltzmann collision operators

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 were 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.

Automated summary

In this work, we explore the possibility of using a deep learning approach to learn from data collision operators for the Lattice Boltzmann Method. We compare different designs of the neural network collision operator and evaluate the resulting LBM method's performance in reproducing time dynamics of canonical flows. The study shows that embedding physical properties can significantly improve the accuracy of the vanilla neural network architecture and correctly reproduce the dynamics of standard fluid flows.