Towards learning a Lattice Boltzmann collisional operator

In this work we explore the possibility of learning a custom collision operator, represented as a deep neural network, for the Lattice Boltzmann method by matching observable data. We present preliminary results in which a neural network is successfully trained as a surrogate of the single relaxation time BGK operator.



We compare the accuracy achieved in the simulation of a few selected benchmarks, employing several approaches for the architecture of the neural network. We show that only by embedding in the neural network physics properties, such as conservation laws and symmetries, it is possible to correctly reproduce the time dynamic of simple fluid flows.