A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs

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

(2020) Eric J. Parish et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism

(2020) Qian Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

(2019) Brian A. Freno et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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

(2019) F. Regazzoni et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

(2019) Kookjin Lee et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Neural network closures for nonlinear model order reduction

(2018) Omer San et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method

(2018) Stefano Pagani et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

(2018) Mengwu Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Hidden physics models: Machine learning of nonlinear partial differential equations

(2018) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

(2018) J.S. Hesthaven et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-assisted reduced-order modeling of extreme events in complex dynamical systems

(2018) Zhong Yi Wan et al.   PLoS One

The Shifted Proper Orthogonal Decomposition: A Mode Decomposition for Multiple Transport Phenomena

(2018) J. Reiss et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven reduced order modeling for time-dependent problems

(2018) Mengwu Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Error modeling for surrogates of dynamical systems using machine learning

(2017) Sumeet Trehan et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Accurate Solution of Bayesian Inverse Uncertainty Quantification Problems Combining Reduced Basis Methods and Reduction Error Models

(2016) A. Manzoni et al.   SIAM-ASA Journal on Uncertainty Quantification

Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction

(2015) David Amsallem et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

(2015) Peter Benner et al.   SIAM REVIEW

Approximated Lax pairs for the reduced order integration of nonlinear evolution equations

(2014) Jean-Frédéric Gerbeau et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Advection modes by optimal mass transfer

(2014) Angelo Iollo et al.   PHYSICAL REVIEW E

The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows

(2013) Kevin Carlberg et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Nonlinear model order reduction based on local reduced-order bases

(2012) David Amsallem et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Nonlinear Model Reduction via Discrete Empirical Interpolation

(2010) Saifon Chaturantabut et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue

(2009) Serdar Göktepe et al.   ARCHIVE OF APPLIED MECHANICS