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.
Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data.Journal of Computational Physics, 514:113261
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S-IDENT identifies nonlinear PDEs from noisy trajectories via noise-adaptive strong-form differentiation with SG-SURE, trimming, and residual-based selection, showing higher noise tolerance than prior strong-form methods and performance comparable to weak-form methods.
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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.
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PDE Identification Using Noise Adaptive Differentiation in Strong Form (S-IDENT)
S-IDENT identifies nonlinear PDEs from noisy trajectories via noise-adaptive strong-form differentiation with SG-SURE, trimming, and residual-based selection, showing higher noise tolerance than prior strong-form methods and performance comparable to weak-form methods.