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.
Multipole graph neural operator for parametric partial differential equations.Advances in Neural Information Processing Systems, 33:6755–6766
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FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
Fredholm Integral Neural Operators are universal approximators of integral operators and are guaranteed to be contractive, enabling reliable solution operator learning for FIEs and PDEs.
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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.
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Learning Contractive Integral Operators with Fredholm Integral Neural Operators
Fredholm Integral Neural Operators are universal approximators of integral operators and are guaranteed to be contractive, enabling reliable solution operator learning for FIEs and PDEs.