Reduced Operator Inference for Nonlinear Partial Differential Equations

DOI10.1137/21M1393972WikidataQ114074100 ScholiaQ114074100MaRDI QIDQ5088794

Karen Willcox, Elizabeth Qian, Ionuţ-Gabriel Farcaş

Publication date: 13 July 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.00083

zbMATH Keywords

nonlinear partial differential equationsscientific machine learningoperator learningnonintrusive model reductiondatadriven modeling

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Linear regression; mixed models (62J05) Learning and adaptive systems in artificial intelligence (68T05) Navier-Stokes equations (35Q30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05) Paired and multiple comparisons; multiple testing (62J15)

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Cites Work

• Unnamed Item
• A kernel-based method for data-driven Koopman spectral analysis
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• Projection-based model reduction: formulations for physics-based machine learning
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems
• Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
• Data-driven operator inference for nonintrusive projection-based model reduction
• Spectral properties of dynamical systems, model reduction and decompositions
• A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations
• Certified Reduced Basis Methods for Parametrized Partial Differential Equations
• Nonlinear Model Reduction via Discrete Empirical Interpolation
• Efficient reduced models anda posteriorierror estimation for parametrized dynamical systems by offline/online decomposition
• Dynamic mode decomposition of numerical and experimental data
• The Random Feature Model for Input-Output Maps between Banach Spaces
• Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
• A ‘best points’ interpolation method for efficient approximation of parametrized functions
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• A PosterioriError Estimation for Reduced-Basis Approximation of Parametrized Elliptic Coercive Partial Differential Equations: “Convex Inverse” Bound Conditioners
• Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
• Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds
• Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
• Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
• Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference
• Data-driven discovery of coordinates and governing equations
• Constrained sparse Galerkin regression
• Two-Sided Projection Methods for Nonlinear Model Order Reduction
• A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations