3 citations · 6 across the 4 of their papers we have counts for
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Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs
Ariel Neufeld, Philipp Schmocker, Sizhou Wu
In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks s…
Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities
Ariel Neufeld, Tuan Anh Nguyen, Sizhou Wu
Neufeld and Wu (arXiv:2310.12545) developed a multilevel Picard (MLP) algorithm which can approximately solve general semilinear parabolic PDEs with gradient-dependent nonlineariti…
Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations
Ariel Neufeld, Tuan Anh Nguyen, Sizhou Wu
In this paper we consider PIDEs with gradient-independent Lipschitz continuous nonlinearities and prove that deep neural networks with ReLU activation function can approximate solu…
Multilevel Picard algorithm for general semilinear parabolic PDEs with gradient-dependent nonlinearities
Ariel Neufeld, Sizhou Wu
In this paper we introduce a multilevel Picard approximation algorithm for general semilinear parabolic PDEs with gradient-dependent nonlinearities whose coefficient functions do n…