Physics-informed machine learning for reduced-order modeling of nonlinear problems

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

(2020) Maziar Raissi et al.   SCIENCE

Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes

(2020) Kazuto Hasegawa et al.   THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS

Learning Physics-Based Reduced-Order Models for a Single-Injector Combustion Process

(2020) Renee Swischuk et al.   AIAA JOURNAL

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

On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows

(2020) Sebastian Grimberg et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics

(2020) Jiayang Xu et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Kolmogorov n-widths for linear dynamical systems

(2019) Benjamin Unger et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

Predictions of turbulent shear flows using deep neural networks

(2019) P. A. Srinivasan et al.   Physical Review Fluids

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

(2019) Luning Sun et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Nonlinear mode decomposition with convolutional neural networks for fluid dynamics

(2019) Takaaki Murata et al.   JOURNAL OF FLUID MECHANICS

Physics-informed neural networks for high-speed flows

(2019) Zhiping Mao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

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

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

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

Model reduction using L 1 -norm minimization as an application to nonlinear hyperbolic problems

(2018) R. Abgrall et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

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

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

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

A dynamic subgrid scale model for Large Eddy Simulations based on the Mori–Zwanzig formalism

(2017) Eric J. Parish et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction

(2017) Kevin Carlberg et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems

(2017) Marie Billaud-Friess et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates

(2015) Benjamin Peherstorfer et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

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

(2015) Peter Benner et al.   SIAM REVIEW

A nonintrusive reduced basis method applied to aeroacoustic simulations

(2014) Fabien Casenave et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

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

Adaptiveh-refinement for reduced-order models

(2014) Kevin Carlberg   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods

(2013) Jan S. Hesthaven et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Entropically damped form of artificial compressibility for explicit simulation of incompressible flow

(2013) Jonathan R. Clausen   PHYSICAL REVIEW E

A Short Review on Model Order Reduction Based on Proper Generalized Decomposition

(2011) Francisco Chinesta et al.   ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING

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

(2011) N. Halko et al.   SIAM REVIEW

Parametric Model Order Reduction by Matrix Interpolation

(2010) Heiko Panzer et al.   AT-Automatisierungstechnik

Nonlinear Model Reduction via Discrete Empirical Interpolation

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

An explicit Chebyshev pseudospectral multigrid method for incompressible Navier–Stokes equations

(2009) W. Zhang et al.   COMPUTERS & FLUIDS

Missing Point Estimation in Models Described by Proper Orthogonal Decomposition

(2008) Patricia Astrid et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL