arXiv：cs.LG· Liyao Lyu, Xinyue Yu, Hayden Schaeffer·· 13 小时前
MVNN：从粒子数据学习 McKean-Vlasov 动力学的测度值神经网络
MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
AI 导读
研究者提出测度值神经网络 MVNN，可直接从粒子轨迹观测中推断依赖测度的交互（漂移）项，通过学习柱状特征将标准神经网络推广到概率测度上。理论上证明了所得动力学的适定性与相关相互作用粒子系统的传播混沌，并在低维测度依赖假设下给出通用逼近与定量逼近速率。
正文
Abstract:Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction (drift) terms directly from particle-trajectory observations. The proposed architecture generalizes standard neural networks to operate on probability measures by learning cylindrical features, using an embedding network that produces scalable distribution-to-vector representations. On the theory side, we establish well-posedness of the resulting dynamics and prove propagation-of-chaos for the associated interacting-particle system. We further show universal approximation and quantitative approximation rates under a low-dimensional measure-dependence assumption. Numerical experiments on first and second order systems, including deterministic and stochastic Motsch-Tadmor dynamics, two-dimensional attraction-repulsion aggregation, Cucker-Smale dynamics, and a hierarchical multi-group system, demonstrate accurate prediction and strong out-of-distribution generalization.
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG); Computational Physics (physics.comp-ph) |
| Cite as: | arXiv:2604.00333 [math.NA] |
| (or arXiv:2604.00333v3 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2604.00333 arXiv-issued DOI via DataCite |
Submission history
From: Liyao Lyu [view email]
[v1]
Wed, 1 Apr 2026 00:11:47 UTC (8,486 KB)
[v2]
Mon, 6 Apr 2026 23:06:42 UTC (8,486 KB)
[v3]
Fri, 9 Oct 2026 06:35:36 UTC (8,611 KB)
来源：arXiv：cs.LG · arxiv.org