  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.
