Data-driven reduced-order modeling of spatiotemporal chaos with neural ordinary differential equations

Revealing the state space of turbulence using machine learning

(2021) Jacob Page et al.   Physical Review Fluids

Discovering Physical Concepts with Neural Networks

(2020) Raban Iten et al.   PHYSICAL REVIEW LETTERS

Structured light entities, chaos and nonlocal maps

(2020) A. Yu Okulov   CHAOS SOLITONS & FRACTALS

Time-series learning of latent-space dynamics for reduced-order model closure

(2020) Romit Maulik et al.   PHYSICA D-NONLINEAR PHENOMENA

Leveraging reduced-order models for state estimation using deep learning

(2020) Nirmal J. Nair et al.   JOURNAL OF FLUID MECHANICS

Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics

(2020) P.R. Vlachas et al.   NEURAL NETWORKS

Convolutional neural network based hierarchical autoencoder for nonlinear mode decomposition of fluid field data

(2020) Kai Fukami et al.   PHYSICS OF FLUIDS

A novel method of low-dimensional representation for temporal behavior of flow fields using deep autoencoder

(2019) Noriyasu Omata et al.   AIP Advances

LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE

(2019) RUSSELL A. EDSON et al.   ANZIAM JOURNAL

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

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

Rapid time series prediction with a hardware-based reservoir computer

(2018) Daniel Canaday et al.   CHAOS

Deep learning for universal linear embeddings of nonlinear dynamics

(2018) Bethany Lusch et al.   Nature Communications

Estimating the Dimension of an Inertial Manifold from Unstable Periodic Orbits

(2016) X. Ding et al.   PHYSICAL REVIEW LETTERS

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

Reduction of SO(2) Symmetry for Spatially Extended Dynamical Systems

(2015) Nazmi Burak Budanur et al.   PHYSICAL REVIEW LETTERS

Inertial manifolds and finite-dimensional reduction for dissipative PDEs

(2014) Sergey Zelik   PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS

Applied Koopmanism

(2012) Marko Budišić et al.   CHAOS

Geometry of Inertial Manifolds Probed via a Lyapunov Projection Method

(2012) Hong-liu Yang et al.   PHYSICAL REVIEW LETTERS

Nonlinear dimensionality reduction in molecular simulation: The diffusion map approach

(2011) Andrew L. Ferguson et al.   CHEMICAL PHYSICS LETTERS

On the State Space Geometry of the Kuramoto–Sivashinsky Flow in a Periodic Domain

(2010) Predrag Cvitanović et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Hyperbolicity and the Effective Dimension of Spatially Extended Dissipative Systems

(2009) Hong-liu Yang et al.   PHYSICAL REVIEW LETTERS