Topological Regularization for Force Prediction in Active Particle Suspension with EGNN and Persistent Homology

Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale collective effects. So we present a multi-scale framework that combines the three learning-driven tools to learn in concert within one pipeline. We use high-resolution Lattice Boltzmann snapshots of fluid velocity and particle stresses in a periodic box as input to the learning pipeline. the second step takes the morphology and positions orientations of particles to predict pairwise interaction forces between them with a E(2)-equivariant graph neural network that necessarily respect flat symmetries. Then, a physics-informed neural network further updates these local estimates by summing over them with a stress data using Fourier feature mappings and residual blocks that is additionally regularized with a topological term (introduced by persistent homology) to penalize unrealistically tangled or spurious connections. In concert, these stages deliver an holistic highly-data driven full force network prediction empathizing on the physical underpinnings together with emerging multi-scale structure typical for active matter.