Neural network approximation

R DeVore, B Hanin, G Petrova - Acta Numerica, 2021 - cambridge.org
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 …

A review of surrogate models and their application to groundwater modeling

MJ Asher, BFW Croke, AJ Jakeman… - Water Resources …, 2015 - Wiley Online Library
The spatially and temporally variable parameters and inputs to complex groundwater
models typically result in long runtimes which hinder comprehensive calibration, sensitivity …

[BOOK][B] Certified reduced basis methods for parametrized partial differential equations

JS Hesthaven, G Rozza, B Stamm - 2016 - Springer
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 …

Non-intrusive reduced order modeling of nonlinear problems using neural networks

JS Hesthaven, S Ubbiali - Journal of Computational Physics, 2018 - Elsevier
We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial
differential equations (PDEs). The method extracts a reduced basis from a collection of high …

[BOOK][B] Numerical models for differential problems

A Quarteroni, S Quarteroni - 2009 - Springer
Alfio Quarteroni Third Edition Page 1 MS&A – Modeling, Simulation and Applications 16
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …

Reduced basis methods for time-dependent problems

JS Hesthaven, C Pagliantini, G Rozza - Acta Numerica, 2022 - cambridge.org
Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

Q Wang, JS Hesthaven, D Ray - Journal of computational physics, 2019 - Elsevier
A non-intrusive reduced-basis (RB) method is proposed for parametrized unsteady flows. A
set of reduced basis functions are extracted from a collection of high-fidelity solutions via a …

Quadratic approximation manifold for mitigating the Kolmogorov barrier in nonlinear projection-based model order reduction

J Barnett, C Farhat - Journal of Computational Physics, 2022 - Elsevier
A quadratic approximation manifold is presented for performing nonlinear, projection-based,
model order reduction (PMOR). It constitutes a departure from the traditional affine subspace …

Convergence rates for greedy algorithms in reduced basis methods

P Binev, A Cohen, W Dahmen, R DeVore… - SIAM journal on …, 2011 - SIAM
The reduced basis method was introduced for the accurate online evaluation of solutions to
a parameter dependent family of elliptic PDEs. Abstractly, it can be viewed as determining a …

Model order reduction in fluid dynamics: challenges and perspectives

T Lassila, A Manzoni, A Quarteroni, G Rozza - Reduced Order Methods for …, 2014 - Springer
This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems
are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit …