Neural networks (NNs) are the method of choice for building learning algorithms. They are
now being investigated for other numerical tasks such as solving high-dimensional partial …

During the past decade, reduced order modeling has attracted growing interest in
computational science and engineering. It now plays an important role in delivering high …

Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

We derive upper bounds on the complexity of ReLU neural networks approximating the
solution maps of parametric partial differential equations. In particular, without any …

Parametric model order reduction using reduced basis methods can be an effective tool for
obtaining quickly solvable reduced order models of parametrized partial differential equation …

Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …

We propose a solution to the problem of quickly and accurately predicting gravitational
waveforms within any given physical model. The method is relevant for both real-time …

The turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …

Numerical relativity simulations provide the most precise templates for the gravitational
waves produced by binary black hole mergers. However, many of these simulations use an …

We present an introduction to some of the state of the art in reduced order and surrogate
modeling in gravitational-wave (GW) science. Approaches that we cover include principal …