From the 1 of 11 linked papers with an AI index.
11 papers
NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes
Anastasis Kratsios, Giulia Livieri, Philipp Schmocker
The paper proposes NeuralChaos, a neural operator architecture that efficiently approximates predictable square‑integrable stochastic processes using finitely many Brownian motion…
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…
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…
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…
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…
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…