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

• URL: http://arxiv.org/abs/2509.06574v1
• Date: Mon, 08 Sep 2025 11:39:42 GMT
• Title: Topological Regularization for Force Prediction in Active Particle Suspension with EGNN and Persistent Homology
• Authors: Sadra Saremi, Amirhossein Ahmadkhan Kordbacheh,
• Abstract summary: We present a multi-scale framework that combines the three learning-driven tools to learn in concert within one pipeline.<n>We use high-resolution Lattice Boltzmann snapshots of fluid velocity and particle stresses in a periodic box as input to the learning pipeline.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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