A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs

S Fresca, L Dede', A Manzoni - Journal of Scientific Computing, 2021 - Springer
Conventional reduced order modeling techniques such as the reduced basis (RB) method
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …

Machine learning for fast and reliable solution of time-dependent differential equations

F Regazzoni, L Dede, A Quarteroni - Journal of Computational physics, 2019 - Elsevier
We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial
Neural Networks (ANNs), applicable to dynamical systems arising from Ordinary Differential …

Method selection in short-term eruption forecasting

MG Whitehead, MS Bebbington - Journal of Volcanology and Geothermal …, 2021 - Elsevier
For accurate and timely information on the evolving state of our volcanoes we need reliable
short-term forecasts. These forecasts directly impact crisis management from evacuations …

A framework for machine learning of model error in dynamical systems

M Levine, A Stuart - Communications of the American Mathematical Society, 2022 - ams.org
The development of data-informed predictive models for dynamical systems is of
widespread interest in many disciplines. We present a unifying framework for blending …

Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism

KK Lin, F Lu - Journal of Computational Physics, 2021 - Elsevier
Abstract Model reduction methods aim to describe complex dynamic phenomena using only
relevant dynamical variables, decreasing computational cost, and potentially highlighting …

[图书][B] Advanced reduced order methods and applications in computational fluid dynamics

G Rozza, G Stabile, F Ballarin - 2022 - SIAM
Reduced order modeling is an important and fast-growing research field in computational
science and engineering, motivated by several reasons, of which we mention just a few …

On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling

F Fritzen, M Fernández, F Larsson - Frontiers in Materials, 2019 - frontiersin.org
A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is
based on the introduction of two different surrogate models and an adaptive on-the-fly …

A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

M Kast, M Guo, JS Hesthaven - Computer Methods in Applied Mechanics …, 2020 - Elsevier
We propose a non-intrusive reduced basis (RB) method for parametrized nonlinear partial
differential equations (PDEs) that leverages models of different accuracy. From a collection …

Time-series machine-learning error models for approximate solutions to parameterized dynamical systems

EJ Parish, KT Carlberg - Computer Methods in Applied Mechanics and …, 2020 - Elsevier
This work proposes a machine-learning framework for modeling the error incurred by
approximate solutions to parameterized dynamical systems. In particular, we extend the …

Evaluation of dual-weighted residual and machine learning error estimation for projection-based reduced-order models of steady partial differential equations

PJ Blonigan, EJ Parish - Computer Methods in Applied Mechanics and …, 2023 - Elsevier
Projection-based reduced-order models (pROMs) show great promise as a means to
accelerate many-query applications such as forward error propagation, solving inverse …