Graph Networks as Inductive Bias for Genetic Programming: Symbolic Models for Particle-Laden Flows

Abstract

High-resolution simulations of particle-laden flows are computationally limited to a scale of thousands of particles due to the complex interactions between particles and fluid. Some approaches to increase the number of particles in such simulations require information about the fluid-induced force on a particle, which is a major challenge in this research area. In this paper, we present an approach to develop symbolic models for the fluid-induced force. We use a graph network as inductive bias to model the underlying pairwise particle interactions. The internal parts of the network are then replaced by symbolic models using a genetic programming algorithm. We include prior problem knowledge in our algorithm. The resulting equations show an accuracy in the same order of magnitude as state-of-the-art approaches for different benchmark datasets. They are interpretable and deliver important building blocks. Our approach is a promising alternative to “black-box” models from the literature.