用拓扑正则化提升活性粒子力预测精度，融合图网络与流体动力学。
Topological Regularization for Force Prediction in Active Particle Suspension with EGNN and Persistent Homology
- 用E(2)等变图网络预测粒子间相互作用力，保持对称性不变。
- 引入持久同调拓扑项，抑制不合理的纠缠连接，提升物理合理性。
- 多尺度联合建模，适合研究活性物质中的集体运动与结构演化。
捕捉活性粒子（自驱动微小颗粒）的动态行为极具挑战，因其需同时考虑精细流体动力学与宏观集体效应。本文提出一个端到端多尺度学习框架，结合三种数据驱动工具：以周期性盒内格子玻尔兹曼模拟的流速和粒子应力快照为输入；第二步利用粒子形态、位置与取向，通过E(2)-等变图神经网络预测成对相互作用力；第三步采用物理信息神经网络，基于傅里叶特征映射与残差块，将局部力估计叠加并使用应力数据进行更新，同时引入持久同调（persistent homology）定义的拓扑正则项，惩罚不合理的缠结或虚假连接。三阶段协同工作，实现高度数据驱动的全力场预测，兼顾物理规律与活性物质典型的多尺度结构特征。
原文摘要 · Abstract (English)
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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