3 citations · 11 across the 13 of their papers we have counts for
14 papers
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with jumps
Ariel Neufeld, Tuan Anh Nguyen, Philipp Schmocker
We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integra…
Approximation rates of quantum neural networks for periodic functions via Jackson's inequality
Ariel Neufeld, Philipp Schmocker, Viet Khoa Tran
Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing, which are represented by a unitary matrix with trainable parameters. In…
Neural Operators Which Certifiably Simultaneously Solve Infinitely Many Convex Programs using Logarithmic Rank and Linear Complexity
Anastasis Kratsios, Ariel Neufeld, Philipp Schmocker
Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whe…
Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion
Ariel Neufeld, Tuan Anh Nguyen, Philipp Schmocker
We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz ass…
Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion
Ariel Neufeld, Philipp Schmocker
In this paper, we solve stochastic partial differential equations (SPDEs) numerically by using (possibly random) neural networks in the truncated Wiener chaos expansion of their co…
Universal approximation results for neural networks with non-polynomial activation function over non-compact domains
Ariel Neufeld, Philipp Schmocker
This paper extends the universal approximation property of single-hidden-layer feedforward neural networks beyond compact domains, which is of particular interest for the approxima…
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in -sense
Ariel Neufeld, Tuan Anh Nguyen
We prove that multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation are capable of approximating solutions of semilinear Kolmogor…
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…
Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations
Ariel Neufeld, Tuan Anh Nguyen
Numerical experiments indicate that deep learning algorithms overcome the curse of dimensionality when approximating solutions of semilinear PDEs. For certain linear PDEs and semil…
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…