POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition

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

(2021) Stefania Fresca et al.   JOURNAL OF SCIENTIFIC COMPUTING

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

(2020) Mariella Kast 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

Deep learning-based reduced order models in cardiac electrophysiology

(2020) Stefania Fresca et al.   PLoS One

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

(2019) Qian Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep ReLU networks and high-order finite element methods

(2019) Joost A. A. Opschoor et al.   Analysis and Applications

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

Reduced-Order Modeling of Subsurface Multi-phase Flow Models Using Deep Residual Recurrent Neural Networks

(2018) J. Nagoor Kani et al.   TRANSPORT IN POROUS MEDIA

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

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

(2018) N. Dal Santo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Data-driven reduced order modeling for time-dependent problems

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

Semi-implicit BDF time discretization of the Navier–Stokes equations with VMS-LES modeling in a High Performance Computing framework

(2015) Davide Forti et al.   COMPUTERS & FLUIDS

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

(2015) Peter Benner et al.   SIAM REVIEW

Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations

(2014) Francesco Ballarin et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants

(2013) Gianluigi Rozza et al.   NUMERISCHE MATHEMATIK

Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

(2011) N. Halko et al.   SIAM REVIEW

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

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