MVNN learns measure-dependent drift terms in McKean-Vlasov equations from particle data using an embedding network, with proofs of well-posedness, propagation of chaos, and universal approximation under low-dimensional assumptions.
A training-free conditional diffusion model for learning stochastic dynamical systems.SIAM Journal on Scientific Computing, 47(5):C1144–C1171
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MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
MVNN learns measure-dependent drift terms in McKean-Vlasov equations from particle data using an embedding network, with proofs of well-posedness, propagation of chaos, and universal approximation under low-dimensional assumptions.