Proves the first universal approximation theorems for k-times differentiable nonlinear operators between Banach spaces and their derivatives uniformly on compact sets in weighted Sobolev norms via encoder-decoder operator learning architectures.
Tackling the curse of dimensionality with physics-informed neural networks.Neural Networks, 176:106369, 2024
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A deep policy iteration method reformulates finite-horizon mean-field games as regenerative problems with deterministic cycles, using particle systems and one-step updates to handle dimensions up to 10,000 efficiently.
citing papers explorer
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Universal Approximation of Nonlinear Operators and Their Derivatives
Proves the first universal approximation theorems for k-times differentiable nonlinear operators between Banach spaces and their derivatives uniformly on compact sets in weighted Sobolev norms via encoder-decoder operator learning architectures.
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Deep Policy Iteration for High-Dimensional Mean-Field Games with Regenerative Reformulation
A deep policy iteration method reformulates finite-horizon mean-field games as regenerative problems with deterministic cycles, using particle systems and one-step updates to handle dimensions up to 10,000 efficiently.