[2604.00333] MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data

Mathematics > Numerical Analysis arXiv:2604.00333 (math) [Submitted on 1 Apr 2026] Title:MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data Authors:Liyao Lyu, Xinyue Yu, Hayden Schaeffer View a PDF of the paper titled MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data, by Liyao Lyu and Xinyue Yu and Hayden Schaeffer View PDF HTML (experimental) 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 accura...