4 papers
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…
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…
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…
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…