Related references
Note: Only part of the references are listed.Modern Koopman Theory for Dynamical Systems
Steven L. Brunton et al.
SIAM REVIEW (2022)
Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification
Diya Sashidhar et al.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2022)
Deep learning models for global coordinate transformations that linearise PDEs
Craig Gin et al.
EUROPEAN JOURNAL OF APPLIED MATHEMATICS (2021)
Sparse identification of multiphase turbulence closures for coupled fluid-particle flows
S. Beetham et al.
JOURNAL OF FLUID MECHANICS (2021)
Learning dominant physical processes with data-driven balance models
Jared L. Callaham et al.
NATURE COMMUNICATIONS (2021)
Galerkin force model for transient and post-transient dynamics of the fluidic pinball
Nan Deng et al.
JOURNAL OF FLUID MECHANICS (2021)
Machine learning-accelerated computational fluid dynamics
Dmitrii Kochkov et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2021)
Nonlinear stochastic modelling with Langevin regression
J. L. Callaham et al.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2021)
Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
Patrick A. K. Reinbold et al.
NATURE COMMUNICATIONS (2021)
Sparse nonlinear models of chaotic electroconvection
Yifei Guan et al.
ROYAL SOCIETY OPEN SCIENCE (2021)
Promoting global stability in data-driven models of quadratic nonlinear dynamics
Alan A. Kaptanoglu et al.
PHYSICAL REVIEW FLUIDS (2021)
Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches
Alan A. Kaptanoglu et al.
PHYSICAL REVIEW E (2021)
Machine Learning for Fluid Mechanics
Steven L. Brunton et al.
ANNUAL REVIEW OF FLUID MECHANICS, VOL 52 (2020)
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
Kookjin Lee et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2020)
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
Elizabeth Qian et al.
PHYSICA D-NONLINEAR PHENOMENA (2020)
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi et al.
SCIENCE (2020)
Physics-Informed Probabilistic Learning of Linear Embeddings of Nonlinear Dynamics with Guaranteed Stability
Shaowu Pan et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2020)
Time -series machine -learning error models for approximate solutions to parameterized dynamical systems
Eric J. Parish et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)
Data-driven modeling of the chaotic thermal convection in an annular thermosyphon
Jean-Christophe Loiseau
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS (2020)
Formulating turbulence closures using sparse regression with embedded form invariance
S. Beetham et al.
PHYSICAL REVIEW FLUIDS (2020)
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
Peter Benner et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)
Using noisy or incomplete data to discover models of spatiotemporal dynamics
Patrick A. K. Reinbold et al.
PHYSICAL REVIEW E (2020)
Discovery of Physics From Data: Universal Laws and Discrepancies
Brian M. de Silva et al.
FRONTIERS IN ARTIFICIAL INTELLIGENCE (2020)
Turbulence Modeling in the Age of Data
Karthik Duraisamy et al.
ANNUAL REVIEW OF FLUID MECHANICS, VOL 51 (2019)
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2019)
Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings
Kathleen P. Champion et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2019)
Linearly Recurrent Autoencoder Networks for Learning Dynamics
Samuel E. Otto et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2019)
Sparse identification of truncation errors
Stephan Thaler et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2019)
Machine learning for fast and reliable solution of time-dependent differential equations
F. Regazzoni et al.
JOURNAL OF COMPUTATIONAL PHYSICS (2019)
Learning data-driven discretizations for partial differential equations
Yohai Bar-Sinai et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2019)
Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning
Frank Noe et al.
SCIENCE (2019)
Robust and optimal sparse regression for nonlinear PDE models
Daniel R. Gurevich et al.
CHAOS (2019)
Data-driven discovery of coordinates and governing equations
Kathleen Champion et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2019)
Perspective on machine learning for advancing fluid mechanics
M. P. Brenner et al.
PHYSICAL REVIEW FLUIDS (2019)
Subgrid modelling for two-dimensional turbulence using neural networks
R. Maulik et al.
JOURNAL OF FLUID MECHANICS (2019)
A Unified Framework for Sparse Relaxed Regularized Regression: SR3
Peng Zheng et al.
IEEE ACCESS (2019)
Sparse learning of stochastic dynamical equations
Lorenzo Boninsegna et al.
JOURNAL OF CHEMICAL PHYSICS (2018)
Sparse reduced-order modelling: sensor-based dynamics to full-state estimation
Jean-Christophe Loiseau et al.
JOURNAL OF FLUID MECHANICS (2018)
Constrained sparse Galerkin regression
Jean-Christophe Loiseau et al.
JOURNAL OF FLUID MECHANICS (2018)
Data-Driven Model Reduction and Transfer Operator Approximation
Stefan Klus et al.
JOURNAL OF NONLINEAR SCIENCE (2018)
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach
Jaideep Pathak et al.
PHYSICAL REVIEW LETTERS (2018)
Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks
Pantelis R. Vlachas et al.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2018)
Koopman analysis of Burgers equation
Jacob Page et al.
PHYSICAL REVIEW FLUIDS (2018)
Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems
J. Nathan Kutz et al.
COMPLEXITY (2018)
Deep learning for universal linear embeddings of nonlinear dynamics
Bethany Lusch et al.
NATURE COMMUNICATIONS (2018)
VAMPnets for deep learning of molecular kinetics (vol 9, 5, 2018)
Andreas Mardt et al.
NATURE COMMUNICATIONS (2018)
Sparse identification of a predator-prey system from simulation data of a convection model
Magnus Dam et al.
PHYSICS OF PLASMAS (2017)
Reconstruction of normal forms by learning informed observation geometries from data
Or Yair et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2017)
Learning partial differential equations via data discovery and sparse optimization
Hayden Schaeffer
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2017)
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
Hassan Arbabi et al.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (2017)
Data-driven discovery of partial differential equations
Samuel H. Rudy et al.
SCIENCE ADVANCES (2017)
Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
Jaideep Pathak et al.
CHAOS (2017)
Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
Qianxiao Li et al.
CHAOS (2017)
Sparse model selection via integral terms
Hayden Schaeffer et al.
PHYSICAL REVIEW E (2017)
Data-driven operator inference for nonintrusive projection-based model reduction
Benjamin Peherstorfer et al.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2016)
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
Julia Ling et al.
JOURNAL OF FLUID MECHANICS (2016)
Observation of Gravitational Waves from a Binary Black Hole Merger
B. P. Abbott et al.
PHYSICAL REVIEW LETTERS (2016)
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Steven L. Brunton et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2016)
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control
Steven L. Brunton et al.
PLOS ONE (2016)
On long-term boundedness of Galerkin models
Michael Schlegel et al.
JOURNAL OF FLUID MECHANICS (2015)
A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
Matthew O. Williams et al.
JOURNAL OF NONLINEAR SCIENCE (2015)
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
Peter Benner et al.
SIAM REVIEW (2015)
Variational Approach to Molecular Kinetics
Feliks Nueske et al.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION (2014)
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
Igor Mezic
ANNUAL REVIEW OF FLUID MECHANICS, VOL 45 (2013)
A VARIATIONAL APPROACH TO MODELING SLOW PROCESSES IN STOCHASTIC DYNAMICAL SYSTEMS
Frank Noe et al.
MULTISCALE MODELING & SIMULATION (2013)
Geometry of the ergodic quotient reveals coherent structures in flows
Marko Budisic et al.
PHYSICA D-NONLINEAR PHENOMENA (2012)
Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability
Dimitrios Giannakis et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2012)
Dynamic mode decomposition of numerical and experimental data
Peter J. Schmid
JOURNAL OF FLUID MECHANICS (2010)
Spectral analysis of nonlinear flows
Clarence W. Rowley et al.
JOURNAL OF FLUID MECHANICS (2009)
Distilling Free-Form Natural Laws from Experimental Data
Michael Schmidt et al.
SCIENCE (2009)
Automated reverse engineering of nonlinear dynamical systems
Josh Bongard et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA (2007)
Spectral properties of dynamical systems, model reduction and decompositions
I Mezic
NONLINEAR DYNAMICS (2005)
Comparison of systems with complex behavior
I Mezic et al.
PHYSICA D-NONLINEAR PHENOMENA (2004)
A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
BR Noack et al.
JOURNAL OF FLUID MECHANICS (2003)
Statistical modeling: The two cultures
L Breiman
STATISTICAL SCIENCE (2001)
Share Paper
