We establish universality and expression rate bounds for a class of neural Deep Operator
Networks (DON) emulating Lipschitz (or H\" older) continuous maps $\mathcal G:\mathcal …

We discuss the calculus of variations in tensor representations with a special focus on tensor
networks and apply it to functionals of practical interest. The survey provides all necessary …

In this article, we describe an efficient approximation of the stochastic Galerkin matrix which
stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed …

In this paper, we suggest approximate algorithms for the reconstruction of sparse high-
dimensional trigonometric polynomials, where the support in frequency domain is unknown …

We consider a framework for the construction of iterative schemes for operator equations
that combine low-rank approximation in tensor formats and adaptive approximation in a …

In this article we propose a novel approach to reduce the computational complexity of the
dual method for pricing American options. We consider a sequence of martingales that …

We generalize the primal–dual methodology, which is popular in the pricing of early‐
exercise options, to a backward dynamic programming equation associated with time …

The hierarchical tensor format allows for the low-parametric representation of tensors even
in high dimensions d. The efficiency of this representation strongly relies on an appropriate …

Biological processes involving the random interaction of d species with integer particle
numbers are often modeled by a Markov jump process on N_0^d. Realizations of this …

Absorbing boundary conditions in the form of a complex absorbing potential are routinely
introduced in the Schrödinger equation to limit the computational domain or to study reactive …