MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
The MVNN framework is a measure-valued neural network designed to learn mean-field interaction terms (drift) directly from particle trajectories. It extends standard neural networks to operate on probability measures by learning cylindrical features, offering a data-driven alternative to traditional kernel estimation. This method provides rigorous theoretical guarantees and successfully predicts complex collective behaviors in various physical and biological systems.