SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

(2020) Maziar Raissi et al.   SCIENCE

Reactive SINDy: Discovering governing reactions from concentration data

(2019) Moritz Hoffmann et al.   JOURNAL OF CHEMICAL PHYSICS

Model selection for hybrid dynamical systems via sparse regression

(2019) N. M. Mangan et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Numerical aspects for approximating governing equations using data

(2019) Kailiang Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Sparse identification of truncation errors

(2019) Stephan Thaler et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven discovery of coordinates and governing equations

(2019) Kathleen Champion et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Sparse identification of nonlinear dynamics for rapid model recovery

(2018) Markus Quade et al.   CHAOS

Control of Complex Nonlinear Dynamic Rational Systems

(2018) Quanmin Zhu et al.   COMPLEXITY

Sparse learning of stochastic dynamical equations

(2018) Lorenzo Boninsegna et al.   JOURNAL OF CHEMICAL PHYSICS

Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

(2018) Christoph Wehmeyer et al.   JOURNAL OF CHEMICAL PHYSICS

Hidden physics models: Machine learning of nonlinear partial differential equations

(2018) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Sparse reduced-order modelling: sensor-based dynamics to full-state estimation

(2018) Jean-Christophe Loiseau et al.   JOURNAL OF FLUID MECHANICS

Constrained sparse Galerkin regression

(2018) Jean-Christophe Loiseau et al.   JOURNAL OF FLUID MECHANICS

Data-Driven Model Reduction and Transfer Operator Approximation

(2018) Stefan Klus et al.   JOURNAL OF NONLINEAR SCIENCE

Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach

(2018) Jaideep Pathak et al.   PHYSICAL REVIEW LETTERS

Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks

(2018) Pantelis R. Vlachas et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

VAMPnets for deep learning of molecular kinetics

(2018) Andreas Mardt et al.   Nature Communications

Data-driven identification of interpretable reduced-order models using sparse regression

(2018) Abhinav Narasingam et al.   COMPUTERS & CHEMICAL ENGINEERING

Robust data-driven discovery of governing physical laws with error bars

(2018) Sheng Zhang et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit

(2018) E. Kaiser et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior

(2018) Zhilu Lai et al.   MECHANICAL SYSTEMS AND SIGNAL PROCESSING

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine learning of linear differential equations using Gaussian processes

(2017) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Sparse identification of a predator-prey system from simulation data of a convection model

(2017) Magnus Dam et al.   PHYSICS OF PLASMAS

Reconstruction of normal forms by learning informed observation geometries from data

(2017) Or Yair et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Model selection for dynamical systems via sparse regression and information criteria

(2017) N. M. Mangan et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems

(2016) Wei Pan et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Sparse identification for nonlinear optical communication systems: SINO method

(2016) Mariia Sorokina et al.   OPTICS EXPRESS

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

(2015) Matthew O. Williams et al.   JOURNAL OF NONLINEAR SCIENCE

Automated adaptive inference of phenomenological dynamical models

(2015) Bryan C. Daniels et al.   Nature Communications

The Optimal Hard Threshold for Singular Values is \(4/\sqrt {3}\)

(2014) Matan Gavish et al.   IEEE TRANSACTIONS ON INFORMATION THEORY

Review of rational (total) nonlinear dynamic system modelling, identification, and control

(2013) Quanmin Zhu et al.   INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE

Analysis of Fluid Flows via Spectral Properties of the Koopman Operator

(2012) Igor Mezić   Annual Review of Fluid Mechanics

Applied Koopmanism

(2012) Marko Budišić et al.   CHAOS

Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability

(2012) Paul D. Arendt et al.   JOURNAL OF MECHANICAL DESIGN

Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability

(2012) D. Giannakis et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

The Original Michaelis Constant: Translation of the 1913 Michaelis–Menten Paper

(2011) Kenneth A. Johnson et al.   BIOCHEMISTRY

Perspectives on system identification

(2010) Lennart Ljung   ANNUAL REVIEWS IN CONTROL

Dynamic mode decomposition of numerical and experimental data

(2010) PETER J. SCHMID   JOURNAL OF FLUID MECHANICS

Robust Face Recognition via Sparse Representation

(2009) J. Wright et al.   IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE

Distilling Free-Form Natural Laws from Experimental Data

(2009) Michael Schmidt et al.   SCIENCE