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

• URL: http://arxiv.org/abs/2604.00333v2
• Date: Mon, 06 Apr 2026 23:06:42 GMT
• Title: MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
• Abstract summary: We introduce a measure-valued neural network that infers measure-dependent interaction terms from particle-trajectory observations.<n>On the theory side, we establish well-posedness of the resulting dynamics and prove propagation-of-chaos for the associated interacting-particle system.<n> Numerical experiments on first and second order systems, including deterministic and 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.
• Score: 0.688204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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