The classical development of neural networks has been primarily for mappings between a
finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional …

We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …

We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation
of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic …

The termsurrogate modeling'in computational science and engineering refers to the
development of computationally efficient approximations for expensive simulations, such as …

Questions of 'how best to acquire data'are essential to modelling and prediction in the
natural and social sciences, engineering applications, and beyond. Optimal experimental …

For a parameter dimension d∈ N, we consider the approximation of many-parametric maps
u:[-1, 1] d→ R by deep ReLU neural networks. The input dimension d may possibly be large …

The classical development of neural networks has been primarily for mappings between a
finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional …

We perform a comprehensive numerical study of the effect of approximation-theoretical
results for neural networks on practical learning problems in the context of numerical …

Neural operator architectures employ neural networks to approximate operators mapping
between Banach spaces of functions; they may be used to accelerate model evaluations via …

In recent work it has been established that deep neural networks (DNNs) are capable of
approximating solutions to a large class of parabolic partial differential equations without …