Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems

DOI10.1016/j.physd.2020.132401zbMath1493.62512arXiv1912.08177OpenAlexW3008005432MaRDI QIDQ2115511

Elizabeth Qian, Benjamin Peherstorfer, Boris Kramer, Karen Willcox

Publication date: 17 March 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.08177

zbMATH Keywords

dynamical systems partial differential equations data-driven model reduction scientific machine learning lifting map

Mathematics Subject Classification ID

Non-Markovian processes: estimation (62M09) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Semilinear parabolic equations (35K58)

Related Items

Learning physics-based models from data: perspectives from inverse problems and model reduction, A data-driven, physics-informed framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings, A New Artificial Neural Network Method for Solving Schrödinger Equations on Unbounded Domains, Model reduction for multi-scale transport problems using model-form preserving least-squares projections with variable transformation, Dynamically learning the parameters of a chaotic system using partial observations, Modern Koopman Theory for Dynamical Systems, Reduced Operator Inference for Nonlinear Partial Differential Equations, Hamiltonian operator inference: physics-preserving learning of reduced-order models for canonical Hamiltonian systems, Operator inference and physics-informed learning of low-dimensional models for incompressible flows, LaSDI: parametric latent space dynamics identification, DRIPS: a framework for dimension reduction and interpolation in parameter space, Multiscale model reduction for incompressible flows, Observer normal form design for the nonlinear MIMO systems using coupled auxiliary dynamics, Output-weighted and relative entropy loss functions for deep learning precursors of extreme events, Canonical and noncanonical Hamiltonian operator inference, Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference, Bayesian operator inference for data-driven reduced-order modeling, SVD perspectives for augmenting DeepONet flexibility and interpretability, Operator inference for non-intrusive model reduction with quadratic manifolds, Regression-Based Projection for Learning Mori–Zwanzig Operators, gLaSDI: parametric physics-informed greedy latent space dynamics identification, Learning Markovian Homogenized Models in Viscoelasticity, A structure-preserving neural differential operator with embedded Hamiltonian constraints for modeling structural dynamics, Active Operator Inference for Learning Low-Dimensional Dynamical-System Models from Noisy Data, Parsimony as the ultimate regularizer for physics-informed machine learning, Structured interpolation for multivariate transfer functions of quadratic-bilinear systems, Operator inference with roll outs for learning reduced models from scarce and low-quality data, Learning to Forecast Dynamical Systems from Streaming Data, Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning, Nonintrusive Reduced-Order Models for Parametric Partial Differential Equations via Data-Driven Operator Inference, Model reduction for stochastic systems with nonlinear drift, Physics-informed ConvNet: learning physical field from a shallow neural network, Reduced order modeling for parametrized generalized Newtonian fluid flows, Discovery of Dynamics Using Linear Multistep Methods, A physics-guided neural network framework for elastic plates: comparison of governing equations-based and energy-based approaches, Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations, Windowed space-time least-squares Petrov-Galerkin model order reduction for nonlinear dynamical systems, Data-driven model order reduction for problems with parameter-dependent jump-discontinuities, A fully adaptive nonintrusive reduced-order modelling approach for parametrized time-dependent problems, Model reduction and neural networks for parametric PDEs, Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories, Non-intrusive data-driven model reduction for differential-algebraic equations derived from lifting transformations, Data-driven resolvent analysis, Intrusive and data-driven reduced order modelling of the rotating thermal shallow water equation, Stability Domains for Quadratic-Bilinear Reduced-Order Models, On the role of nonlinear correlations in reduced-order modelling, Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference, Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

Cites Work