Topological Regularization for Force Prediction in Active Particle Suspension with EGNN and Persistent Homology
This work addresses the challenge of modeling active particle dynamics for researchers in soft matter physics and fluid dynamics, representing an incremental improvement through integration of existing methods.
The paper tackled the problem of predicting interaction forces in active particle suspensions by developing a multi-scale framework that combines an E(2)-equivariant graph neural network, a physics-informed neural network, and topological regularization, achieving a holistic force network prediction that emphasizes physical underpinnings and multi-scale structure.
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.