3 citations · 11 across the 13 of their papers we have counts for
5 papers · 1 filter
Universal approximation property of Banach space-valued random feature models including random neural networks
Ariel Neufeld, Philipp Schmocker
We introduce a Banach space-valued extension of random feature learning, a data-driven supervised machine learning technique for large-scale kernel approximation. By randomly initi…
Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean--Vlasov stochastic differential equations
Ariel Neufeld, Tuan Anh Nguyen
In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean--Vlasov SDEs in the sense that the number of par…
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…