Data-Driven Reduced Model Construction with Time-Domain Loewner Models

DOI10.1137/16M1094750zbMath1448.65087OpenAlexW2759838493MaRDI QIDQ5364198

Karen Willcox, Benjamin Peherstorfer, Serkan Gugercin

Publication date: 4 October 2017

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

Full work available at URL: https://doi.org/10.1137/16m1094750

zbMATH Keywords

dynamical systemspartial differential equationsdata-driven model reductionLoewner frameworkblack-box modelsnonintrusive model reductionprojection-based reduced models

Mathematics Subject Classification ID

System structure simplification (93B11) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for differential-algebraic equations (65L80)

Related Items (25)

Data-Driven Balancing of Linear Dynamical Systems ⋮ A data-driven, physics-informed framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings ⋮ Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation ⋮ Model order reduction method based on (r)POD-ANNs for parameterized time-dependent partial differential equations ⋮ Retracted: Model order reduction method based on machine learning for parameterized time-dependent partial differential equations ⋮ Operator inference and physics-informed learning of low-dimensional models for incompressible flows ⋮ A non-intrusive method to inferring linear port-Hamiltonian realizations using time-domain data ⋮ A non‐linear non‐intrusive reduced order model of fluid flow by auto‐encoder and self‐attention deep learning methods ⋮ Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference ⋮ Port-Hamiltonian Dynamic Mode Decomposition ⋮ Operator inference with roll outs for learning reduced models from scarce and low-quality data ⋮ A data-driven Krylov model order reduction for large-scale dynamical systems ⋮ Data-driven constrained optimal model reduction ⋮ Identification of port-Hamiltonian systems from frequency response data ⋮ Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models ⋮ Machine learning for fast and reliable solution of time-dependent differential equations ⋮ Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference ⋮ Projection-based model reduction: formulations for physics-based machine learning ⋮ Minimal realization and approximation of commensurate linear fractional-order systems via Loewner matrix method ⋮ A fully adaptive nonintrusive reduced-order modelling approach for parametrized time-dependent problems ⋮ Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms ⋮ 6 The Loewner framework for system identification and reduction ⋮ Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations ⋮ Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation ⋮ On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

Uses Software

• Loewner

Cites Work

• Unnamed Item
• Unnamed Item
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• A model-data weak formulation for simultaneous estimation of state and model bias
• Model reduction for systems with inhomogeneous initial conditions
• System identification methods for (operational) modal analysis: review and comparison
• Balanced truncation model reduction for systems with inhomogeneous initial conditions
• The Loewner framework and transfer functions of singular/rectangular systems
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• A framework for the solution of the generalized realization problem
• A family of embedded Runge-Kutta formulae
• Subspace-based methods for the identification of linear time-invariant systems
• Data-driven operator inference for nonintrusive projection-based model reduction
• A paradigm for data-driven predictive modeling using field inversion and machine learning
• Algorithms for model reduction of large dynamical systems
• On dynamic mode decomposition: theory and applications
• PBDW State Estimation: Noisy Observations; Configuration-Adaptive Background Spaces; Physical Interpretations
• Dynamic Mode Decomposition with Control
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Tangential interpolation-based eigensystem realization algorithm for MIMO systems
• Distributed control of linearized Navier-Stokes equations via discretized input/output maps
• Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation
• Interpolatory Model Reduction of Large-Scale Dynamical Systems
• FIR system modeling and identification in the presence of noise and with band-limited inputs
• Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
• Hessian-based model reduction for large-scale systems with initial-condition inputs
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• On the Scalar Rational Interpolation Problem
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Synthesis of minimum roundoff noise fixed point digital filters
• Dynamic mode decomposition for financial trading strategies
• Interpolation-Based ${\cal H}_2$-Model Reduction of Bilinear Control Systems
• Reduced basis method for finite volume approximations of parametrized linear evolution equations
• Chapter 2: Regularization of Linear and Nonlinear Descriptor Systems
• Approximation of Large-Scale Dynamical Systems

This page was built for publication: Data-Driven Reduced Model Construction with Time-Domain Loewner Models