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

One of our DFG-funded projects addresses Genetic Programming (GP) for a problem from fluid mechanics: We develop algorithms to identify symbolic models for the complex particle-particle and particle-fluid interactions in particle-laden flows. Such flows occur in many real-world applications, such as the fluidization of biomass particles in furnaces, or the flow of blood cells in blood plasma. One challenge is the huge number of interactions considered when billions of particles are involved. Recent studies indicate that machine learning models do not improve further when more than 30 neighboring particles are considered in the prediction of the force exerted on a particle. In other words, to predict the force on a particle, we solely need to consider the locations of its 30 closest neighbors.

In our current work, we created benchmark datasets for the force on a center particle, given the locations of its 30 closest neighbors. The interactions between particles are modeled as a directed graph, which has one outgoing edge from all neighbors towards the center particle. We induce a bias by approximating the underlying relations with a Graph Network (GN), where the influences of neighboring particles are aggregated by a sum in order to compute the force on the center particle. In the next step, the network blocks of the GN are replaced by symbolic models.

Have a look at our results and learnings from this experiment.