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.
Fourier neural operator for parametric partial differential equations
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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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FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation
FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.