A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Gradient-based constrained optimization using a database of linear reduced-order models

(2020) Youngsoo Choi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

(2019) Christian Beck et al.   JOURNAL OF NONLINEAR SCIENCE

Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction

(2019) Youngsoo Choi et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

(2019) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang 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

Conservative model reduction for finite-volume models

(2018) Kevin Carlberg et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The Discrete Empirical Interpolation Method: Canonical Structure and Formulation in Weighted Inner Product Spaces

(2018) Zlatko Drmač et al.   SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS

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

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

Transport Reversal for Model Reduction of Hyperbolic Partial Differential Equations

(2018) Donsub Rim et al.   SIAM-ASA Journal on Uncertainty Quantification

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A unified deep artificial neural network approach to partial differential equations in complex geometries

(2018) Jens Berg et al.   NEUROCOMPUTING

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Implementation and detailed assessment of a GNAT reduced-order model for subsurface flow simulation

(2018) Rui Jiang 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

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

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

POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification

(2017) Hongfei Fu et al.   JOURNAL OF SCIENTIFIC COMPUTING

POD-DEIM reduction of computational EMG models

(2017) M. Mordhorst et al.   Journal of Computational Science

A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions

(2016) Zlatko Drmač et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Fast Multiscale Reservoir Simulations With POD-DEIM Model Reduction

(2016) Yanfang Yang et al.   SPE JOURNAL

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

(2015) Peter Benner et al.   SIAM REVIEW

Adaptiveh-refinement for reduced-order models

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

Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

(2014) D. Xiao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Design optimization using hyper-reduced-order models

(2014) David Amsallem et al.   STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION

POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization

(2014) Pengfei Zhao et al.   Journal of Applied Mathematics

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

POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model

(2012) R. Ştefănescu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations

(2010) Kevin Carlberg et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Reduced order modeling based shape optimization of surface acoustic wave driven microfluidic biochips

(2010) Harbir Antil et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Nonlinear Model Reduction via Discrete Empirical Interpolation

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