5 citations · 12 across the 12 of their papers we have counts for
13 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…
Neural operators approximate strongly continuous convex monotone semigroups
Jonas Blessing, Philipp Schmocker, Alessandro Sgarabottolo
We approximate strongly continuous convex monotone semigroups by learning their Chernoff-type one-step operators with neural operators. First, we introduce the general class of so-…
NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes
Anastasis Kratsios, Giulia Livieri, Philipp Schmocker
We address fundamental challenges in representing and computing -valued predictable square-integrable processes over , collected in the space $\mathcal{H}^2_…
Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
Philipp Schmocker, Josef Teichmann
We generalize the universal approximation theorem for functional input neural networks (FNN) to differentiable maps by including the approximation of the derivatives. A FNN maps th…
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…
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…
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…
Global universal approximation of functional input maps on weighted spaces
Christa Cuchiero, Philipp Schmocker, Josef Teichmann
We introduce so-called functional input neural networks defined on a possibly infinite dimensional weighted space with values also in a possibly infinite dimensional output space.…
Chaotic Hedging with Iterated Integrals and Neural Networks
Ariel Neufeld, Philipp Schmocker
In this paper, we derive an -chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable continuous semimartingale. By omitting t…