Discovering governing equations from partial measurements with deep delay autoencoders

Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions

(2023) Paolo Conti et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Model selection of chaotic systems from data with hidden variables using sparse data assimilation

(2022) H. Ribera et al.   CHAOS

Discovering sparse interpretable dynamics from partial observations

(2022) Peter Y. Lu et al.   Communications Physics

Data-driven discovery of coarse-grained equations

(2021) Joseph Bakarji et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression

(2021) Patrick A. K. Reinbold et al.   Nature Communications

Structured time-delay models for dynamical systems with connections to Frenet–Serret frame

(2021) Seth M. Hirsh et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

On the structure of time-delay embedding in linear models of non-linear dynamical systems

(2020) Shaowu Pan et al.   CHAOS

Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits

(2020) Balachandra Suri et al.   PHYSICAL REVIEW LETTERS

Formulating turbulence closures using sparse regression with embedded form invariance

(2020) S. Beetham et al.   Physical Review Fluids

Linearly Recurrent Autoencoder Networks for Learning Dynamics

(2019) Samuel E. Otto et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Delay-Coordinate Maps and the Spectra of Koopman Operators

(2019) Suddhasattwa Das et al.   JOURNAL OF STATISTICAL PHYSICS

Inferring causation from time series in Earth system sciences

(2019) Jakob Runge et al.   Nature Communications

Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion

(2019) Seungjoon Lee et al.   Interface Focus

Robust and optimal sparse regression for nonlinear PDE models

(2019) Daniel R. Gurevich et al.   CHAOS

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

Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

(2019) Martin Schmelzer et al.   FLOW TURBULENCE AND COMBUSTION

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

(2019) Kookjin Lee et al.   JOURNAL OF COMPUTATIONAL PHYSICS

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

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

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

Turbulence Modeling in the Age of Data

(2018) Karthik Duraisamy et al.   Annual Review of Fluid Mechanics

Complex network approaches to nonlinear time series analysis

(2018) Yong Zou et al.   PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS

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

Deep learning for universal linear embeddings of nonlinear dynamics

(2018) Bethany Lusch et al.   Nature Communications

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

Chaos as an intermittently forced linear system

(2017) Steven L. Brunton et al.   Nature Communications

Data-driven spectral decomposition and forecasting of ergodic dynamical systems

(2017) Dimitrios Giannakis   APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS

Extracting spatial–temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition

(2016) Bingni W. Brunton et al.   JOURNAL OF NEUROSCIENCE METHODS

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

Automated adaptive inference of phenomenological dynamical models

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

Distinguishing time-delayed causal interactions using convergent cross mapping

(2015) Hao Ye et al.   Scientific Reports

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

Detecting Causality in Complex Ecosystems

(2012) G. Sugihara et al.   SCIENCE

Dynamic mode decomposition of numerical and experimental data

(2010) PETER J. SCHMID   JOURNAL OF FLUID MECHANICS

Distilling Free-Form Natural Laws from Experimental Data

(2009) Michael Schmidt et al.   SCIENCE