Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems

Optimal Stable Nonlinear Approximation

(2021) Albert Cohen et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces.

(2020) Virginie Ehrlacher et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Dimensionality reduction and reduced-order modeling for traveling wave physics

(2020) Ariana Mendible et al.   THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS

Projection-based model reduction with dynamically transformed modes

(2020) Felix Black et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Kolmogorov n-widths for linear dynamical systems

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

A characteristic dynamic mode decomposition

(2019) Jörn Sesterhenn et al.   THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS

Decay of the Kolmogorov N-width for wave problems

(2019) Constantin Greif et al.   APPLIED MATHEMATICS LETTERS

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

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

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

Transported snapshot model order reduction approach for parametric, steady-state fluid flows containing parameter-dependent shocks

(2018) Nirmal J. Nair et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Interpolation of Functions with Parameter Dependent Jumps by Transformed Snapshots

(2017) G. Welper   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Reduced basis techniques for nonlinear conservation laws

(2015) T. Taddei et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

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

Adaptiveh-refinement for reduced-order models

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

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

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

A space-time hp-interpolation-based certified reduced basis method for Burgers' equation

(2014) Masayuki Yano et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Advection modes by optimal mass transfer

(2014) Angelo Iollo et al.   PHYSICAL REVIEW E

Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing

(2013) Mario Ohlberger et al.   COMPTES RENDUS MATHEMATIQUE

Nonlinear Model Reduction via Discrete Empirical Interpolation

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

Dynamically orthogonal field equations for continuous stochastic dynamical systems

(2009) Themistoklis P. Sapsis et al.   PHYSICA D-NONLINEAR PHENOMENA