Operator inference for non-intrusive model reduction with quadratic manifolds

Geelen, Rudy; Wright, Stephen; Willcox, Karen

doi:10.1016/j.cma.2022.115717

Title: Operator inference for non-intrusive model reduction with quadratic manifolds

Abstract

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.

Authors:

^[1]; Wright, Stephen ^[2]; Willcox, Karen ^[1]

Univ. of Texas, Austin, TX (United States). Oden Institute for Computational Engineering and Sciences
Univ. of Wisconsin, Madison, WI (United States)

Publication Date:: Sat Nov 19 00:00:00 EST 2022

Research Org.:: Univ. of Texas, Austin, TX (United States). Oden Institute for Computational Engineering and Sciences; Univ. of Texas, Austin, TX (United States)

Sponsoring Org.:: USDOE; US Air Force Office of Scientific Research (AFOSR)

OSTI Identifier:: 1905877

Alternate Identifier(s):: OSTI ID: 1899717; OSTI ID: 2340144

Grant/Contract Number:: SC0019303; FA9550-21-1-0084

Resource Type:: Accepted Manuscript

Journal Name:: Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:: Journal Volume: 403; Journal ID: ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Data-driven model reduction; Nonlinear manifolds; Operator inference; Proper orthogonal decomposition

Citation Formats


                    Geelen, Rudy, Wright, Stephen, and Willcox, Karen. Operator inference for non-intrusive model reduction with quadratic manifolds.  United States: N. p., 2022. 
Web.  doi:10.1016/j.cma.2022.115717.

Copy to clipboard


                    Geelen, Rudy, Wright, Stephen, & Willcox, Karen. Operator inference for non-intrusive model reduction with quadratic manifolds.  United States.  https://doi.org/10.1016/j.cma.2022.115717

Copy to clipboard


                    Geelen, Rudy, Wright, Stephen, and Willcox, Karen. Sat .  
"Operator inference for non-intrusive model reduction with quadratic manifolds".  United States.  https://doi.org/10.1016/j.cma.2022.115717.  https://www.osti.gov/servlets/purl/1905877.

Copy to clipboard


                    
@article{osti_1905877,

  title        = {Operator inference for non-intrusive model reduction with quadratic manifolds},

  author       = {Geelen, Rudy and Wright, Stephen and Willcox, Karen},

  abstractNote = {This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.},

  doi          = {10.1016/j.cma.2022.115717},

  journal      = {Computer Methods in Applied Mechanics and Engineering},

  number       = ,

  volume       = 403,

  place        = {United States},

  year         = {Sat Nov 19 00:00:00 EST 2022},

  month        = {Sat Nov 19 00:00:00 EST 2022}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1016/j.cma.2022.115717

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Model order reduction assisted by deep neural networks (ROM-net)
journal, April 2020

Daniel, Thomas; Casenave, Fabien; Akkari, Nissrine
Advanced Modeling and Simulation in Engineering Sciences, Vol. 7, Issue 1
DOI: 10.1186/s40323-020-00153-6

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization
journal, April 2022

Baddoo, Peter J.; Herrmann, Benjamin; McKeon, Beverley J.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 478, Issue 2260
DOI: 10.1098/rspa.2021.0830

Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
journal, May 2022

Peherstorfer, Benjamin
Notices of the American Mathematical Society, Vol. 69, Issue 05
DOI: 10.1090/noti2475

Sparse Reconstruction by Separable Approximation
journal, July 2009

Wright, S. J.; Nowak, R. D.; Figueiredo, M. A. T.
IEEE Transactions on Signal Processing, Vol. 57, Issue 7
DOI: 10.1109/TSP.2009.2016892

Nonlinear dimensionality reduction for parametric problems: A kernel proper orthogonal decomposition
journal, October 2021

Díez, Pedro; Muixí, Alba; Zlotnik, Sergio
International Journal for Numerical Methods in Engineering, Vol. 122, Issue 24
DOI: 10.1002/nme.6831

Nonlinear model order reduction based on local reduced-order bases: NONLINEAR MODEL REDUCTION BASED ON LOCAL REDUCED-ORDER BASES
journal, June 2012

Amsallem, David; Zahr, Matthew J.; Farhat, Charbel
International Journal for Numerical Methods in Engineering, Vol. 92, Issue 10
DOI: 10.1002/nme.4371

A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism
journal, September 2017

Gouasmi, Ayoub; Parish, Eric J.; Duraisamy, Karthik
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2205
DOI: 10.1098/rspa.2017.0385

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
journal, May 2020

Qian, Elizabeth; Kramer, Boris; Peherstorfer, Benjamin
Physica D: Nonlinear Phenomena, Vol. 406
DOI: 10.1016/j.physd.2020.132401

Interpolation of Functions with Parameter Dependent Jumps by Transformed Snapshots
journal, January 2017

Welper, G.
SIAM Journal on Scientific Computing, Vol. 39, Issue 4
DOI: 10.1137/16M1059904

Data-Driven Discovery of Closure Models
journal, January 2018

Pan, Shaowu; Duraisamy, Karthik
SIAM Journal on Applied Dynamical Systems, Vol. 17, Issue 4
DOI: 10.1137/18M1177263

Localized Discrete Empirical Interpolation Method
journal, January 2014

Peherstorfer, Benjamin; Butnaru, Daniel; Willcox, Karen
SIAM Journal on Scientific Computing, Vol. 36, Issue 1
DOI: 10.1137/130924408

Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
journal, December 2013

Ohlberger, Mario; Rave, Stephan
Comptes Rendus Mathematique, Vol. 351, Issue 23-24
DOI: 10.1016/j.crma.2013.10.028

Data-driven operator inference for nonintrusive projection-based model reduction
journal, July 2016

Peherstorfer, Benjamin; Willcox, Karen
Computer Methods in Applied Mechanics and Engineering, Vol. 306
DOI: 10.1016/j.cma.2016.03.025

A quadratic manifold for model order reduction of nonlinear structural dynamics
journal, August 2017

Jain, Shobhit; Tiso, Paolo; Rutzmoser, Johannes B.
Computers & Structures, Vol. 188
DOI: 10.1016/j.compstruc.2017.04.005

Simultaneous Variable Selection
journal, August 2005

Turlach, Berwin A.; Venables, William N.; Wright, Stephen J.
Technometrics, Vol. 47, Issue 3
DOI: 10.1198/004017005000000139

Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs
journal, January 2021

Taddei, Tommaso; Zhang, Lei
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 55, Issue 1
DOI: 10.1051/m2an/2020073

Advection modes by optimal mass transfer
journal, February 2014

Iollo, Angelo; Lombardi, Damiano
Physical Review E, Vol. 89, Issue 2
DOI: 10.1103/PhysRevE.89.022923

A Registration Method for Model Order Reduction: Data Compression and Geometry Reduction
journal, January 2020

Taddei, Tommaso
SIAM Journal on Scientific Computing, Vol. 42, Issue 2
DOI: 10.1137/19M1271270

Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process
journal, January 2021

McQuarrie, Shane A.; Huang, Cheng; Willcox, Karen E.
Journal of the Royal Society of New Zealand, Vol. 51, Issue 2
DOI: 10.1080/03036758.2020.1863237

LIII. On lines and planes of closest fit to systems of points in space
journal, November 1901

Pearson, Karl
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 2, Issue 11
DOI: 10.1080/14786440109462720

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference
journal, January 2020

Peherstorfer, Benjamin
SIAM Journal on Scientific Computing, Vol. 42, Issue 5
DOI: 10.1137/19M1292448

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques
journal, February 2022

Kadeethum, T.; Ballarin, F.; Choi, Y.
Advances in Water Resources, Vol. 160
DOI: 10.1016/j.advwatres.2021.104098

Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks
journal, December 2021

Salvador, M.; Dedè, L.; Manzoni, A.
Computers & Mathematics with Applications, Vol. 104
DOI: 10.1016/j.camwa.2021.11.001

Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems
journal, March 2022

Sharma, Harsh; Wang, Zhu; Kramer, Boris
Physica D: Nonlinear Phenomena, Vol. 431
DOI: 10.1016/j.physd.2021.133122

On closures for reduced order models—A spectrum of first-principle to machine-learned avenues
journal, September 2021

Ahmed, Shady E.; Pawar, Suraj; San, Omer
Physics of Fluids, Vol. 33, Issue 9
DOI: 10.1063/5.0061577

The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
journal, January 1993

Berkooz, G.; Holmes, P.; Lumley, J. L.
Annual Review of Fluid Mechanics, Vol. 25, Issue 1
DOI: 10.1146/annurev.fl.25.010193.002543

Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics
journal, November 2017

Rutzmoser, J. B.; Rixen, D. J.; Tiso, P.
Computers & Structures, Vol. 192
DOI: 10.1016/j.compstruc.2017.06.003

Adaptive h -refinement for reduced-order models : ADAPTIVE
journal, November 2014

Carlberg, Kevin
International Journal for Numerical Methods in Engineering, Vol. 102, Issue 5
DOI: 10.1002/nme.4800

Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter-dependent shocks: Model order reduction for fluid flows containing shocks
journal, December 2018

Nair, Nirmal J.; Balajewicz, Maciej
International Journal for Numerical Methods in Engineering, Vol. 117, Issue 12
DOI: 10.1002/nme.5998

Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling
journal, January 2020

Peherstorfer, Benjamin
SIAM Journal on Scientific Computing, Vol. 42, Issue 5
DOI: 10.1137/19M1257275

A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs
journal, April 2021

Fresca, Stefania; Dede’, Luca; Manzoni, Andrea
Journal of Scientific Computing, Vol. 87, Issue 2
DOI: 10.1007/s10915-021-01462-7

Nonlinear proper orthogonal decomposition for convection-dominated flows
journal, December 2021

Ahmed, Shady E.; San, Omer; Rasheed, Adil
Physics of Fluids, Vol. 33, Issue 12
DOI: 10.1063/5.0074310

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
journal, December 2020

Benner, Peter; Goyal, Pawan; Kramer, Boris
Computer Methods in Applied Mechanics and Engineering, Vol. 372
DOI: 10.1016/j.cma.2020.113433

Projection-based model reduction with dynamically transformed modes
journal, October 2020

Black, Felix; Schulze, Philipp; Unger, Benjamin
ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 54, Issue 6
DOI: 10.1051/m2an/2020046

Turbulence and the dynamics of coherent structures. I. Coherent structures
journal, January 1987

Sirovich, Lawrence
Quarterly of Applied Mathematics, Vol. 45, Issue 3
DOI: 10.1090/qam/910462

Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition
journal, June 2019

Kramer, Boris; Willcox, Karen E.
AIAA Journal, Vol. 57, Issue 6
DOI: 10.2514/1.J057791

Learning physics-based models from data: perspectives from inverse problems and model reduction
journal, May 2021

Ghattas, Omar; Willcox, Karen
Acta Numerica, Vol. 30
DOI: 10.1017/S0962492921000064

Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
journal, November 2020

Gao, Han; Wang, Jian-Xun; Zahr, Matthew J.
Physica D: Nonlinear Phenomena, Vol. 412
DOI: 10.1016/j.physd.2020.132614

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
journal, November 2019

Lee, Kookjin; Carlberg, Kevin T.
Journal of Computational Physics
DOI: 10.1016/j.jcp.2019.108973

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison
journal, September 2012

Wang, Zhu; Akhtar, Imran; Borggaard, Jeff
Computer Methods in Applied Mechanics and Engineering, Vol. 237-240
DOI: 10.1016/j.cma.2012.04.015

An Explicit Nonlinear Mapping for Manifold Learning
journal, February 2013

Hong Qiao,
IEEE Transactions on Cybernetics, Vol. 43, Issue 1
DOI: 10.1109/TSMCB.2012.2198916

Similar Records in DOE PAGES and OSTI.GOV collections:

Learning physics-based reduced-order models from data using nonlinear manifolds

Journal Article Geelen, Rudy ; Balzano, Laura ; Wright, Stephen ; ... - Chaos: An Interdisciplinary Journal of Nonlinear Science

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracymore »« less
https://doi.org/10.1063/5.0170105
Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

Journal Article Kadeethum, Teeratorn ; Ballarin, Francesco ; O’Malley, Daniel ; ... - Scientific Reports

Absmore »« less
https://doi.org/10.1038/s41598-022-24545-3
Non-Intrusive Inference Reduced Order Model for Fluids Using Deep Multistep Neural Network

Journal Article Xie, Xuping ; Zhang, Guannan ; Webster, Clayton G. - Mathematics

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical engineering applications. Classical projection-based model reduction methods generate reduced systems by projecting full-order differential operators into low-dimensional subspaces. However, these techniques usually lead to severe instabilities in the presence of highly nonlinear dynamics, which dramatically deteriorates the accuracy of the reduced-order models. In contrast, our new framework exploits linear multistep networks, based on implicit Adams–Moulton schemes, to construct the reduced system. The advantage is that the methodmore »« less
Cited by 15
https://doi.org/10.3390/math7080757
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

Journal Article Qian, Elizabeth ; Kramer, Boris ; Peherstorfer, Benjamin ; ... - Physica. D, Nonlinear Phenomena

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data usingmore »« less
Cited by 95
https://doi.org/10.1016/j.physd.2020.132401

Full Text Available
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms

Journal Article Benner, Peter ; Goyal, Pawan ; Kramer, Boris ; ... - Computer Methods in Applied Mechanics and Engineering

Here in this work we present a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear andmore »« less
https://doi.org/10.1016/j.cma.2020.113433

Full Text Available

Similar Records

Title: Operator inference for non-intrusive model reduction with quadratic manifolds

Abstract

Citation Formats

Model order reduction assisted by deep neural networks (ROM-net) journal, April 2020

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization journal, April 2022

Breaking the Kolmogorov Barrier with Nonlinear Model Reduction journal, May 2022

Sparse Reconstruction by Separable Approximation journal, July 2009

Nonlinear dimensionality reduction for parametric problems: A kernel proper orthogonal decomposition journal, October 2021

Nonlinear model order reduction based on local reduced-order bases: NONLINEAR MODEL REDUCTION BASED ON LOCAL REDUCED-ORDER BASES journal, June 2012

A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism journal, September 2017

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems journal, May 2020

Interpolation of Functions with Parameter Dependent Jumps by Transformed Snapshots journal, January 2017

Data-Driven Discovery of Closure Models journal, January 2018

Localized Discrete Empirical Interpolation Method journal, January 2014

Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing journal, December 2013

Data-driven operator inference for nonintrusive projection-based model reduction journal, July 2016

A quadratic manifold for model order reduction of nonlinear structural dynamics journal, August 2017

Simultaneous Variable Selection journal, August 2005

Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs journal, January 2021

Advection modes by optimal mass transfer journal, February 2014

A Registration Method for Model Order Reduction: Data Compression and Geometry Reduction journal, January 2020

Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process journal, January 2021

LIII. On lines and planes of closest fit to systems of points in space journal, November 1901

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference journal, January 2020

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques journal, February 2022

Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks journal, December 2021

Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems journal, March 2022

On closures for reduced order models—A spectrum of first-principle to machine-learned avenues journal, September 2021

The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows journal, January 1993

Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics journal, November 2017

Adaptive h -refinement for reduced-order models : ADAPTIVE journal, November 2014

Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter-dependent shocks: Model order reduction for fluid flows containing shocks journal, December 2018

Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling journal, January 2020

A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs journal, April 2021

Nonlinear proper orthogonal decomposition for convection-dominated flows journal, December 2021

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms journal, December 2020

Projection-based model reduction with dynamically transformed modes journal, October 2020

Turbulence and the dynamics of coherent structures. I. Coherent structures journal, January 1987

Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition journal, June 2019

Learning physics-based models from data: perspectives from inverse problems and model reduction journal, May 2021

Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning journal, November 2020

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders journal, November 2019

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison journal, September 2012

An Explicit Nonlinear Mapping for Manifold Learning journal, February 2013

Model order reduction assisted by deep neural networks (ROM-net)
journal, April 2020

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization
journal, April 2022

Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
journal, May 2022

Sparse Reconstruction by Separable Approximation
journal, July 2009

Nonlinear dimensionality reduction for parametric problems: A kernel proper orthogonal decomposition
journal, October 2021

Nonlinear model order reduction based on local reduced-order bases: NONLINEAR MODEL REDUCTION BASED ON LOCAL REDUCED-ORDER BASES
journal, June 2012

A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism
journal, September 2017

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
journal, May 2020

Interpolation of Functions with Parameter Dependent Jumps by Transformed Snapshots
journal, January 2017

Data-Driven Discovery of Closure Models
journal, January 2018

Localized Discrete Empirical Interpolation Method
journal, January 2014

Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing
journal, December 2013

Data-driven operator inference for nonintrusive projection-based model reduction
journal, July 2016

A quadratic manifold for model order reduction of nonlinear structural dynamics
journal, August 2017

Simultaneous Variable Selection
journal, August 2005

Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs
journal, January 2021

Advection modes by optimal mass transfer
journal, February 2014

A Registration Method for Model Order Reduction: Data Compression and Geometry Reduction
journal, January 2020

Data-driven reduced-order models via regularised Operator Inference for a single-injector combustion process
journal, January 2021

LIII. On lines and planes of closest fit to systems of points in space
journal, November 1901

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference
journal, January 2020

Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques
journal, February 2022

Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks
journal, December 2021

Hamiltonian operator inference: Physics-preserving learning of reduced-order models for canonical Hamiltonian systems
journal, March 2022

On closures for reduced order models—A spectrum of first-principle to machine-learned avenues
journal, September 2021

The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
journal, January 1993

Generalization of quadratic manifolds for reduced order modeling of nonlinear structural dynamics
journal, November 2017

Adaptive h -refinement for reduced-order models : ADAPTIVE
journal, November 2014

Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter-dependent shocks: Model order reduction for fluid flows containing shocks
journal, December 2018

Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling
journal, January 2020

A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs
journal, April 2021

Nonlinear proper orthogonal decomposition for convection-dominated flows
journal, December 2021

Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
journal, December 2020

Projection-based model reduction with dynamically transformed modes
journal, October 2020

Turbulence and the dynamics of coherent structures. I. Coherent structures
journal, January 1987

Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition
journal, June 2019

Learning physics-based models from data: perspectives from inverse problems and model reduction
journal, May 2021

Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
journal, November 2020

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
journal, November 2019

Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison
journal, September 2012

An Explicit Nonlinear Mapping for Manifold Learning
journal, February 2013