Regression-Based Projection for Learning Mori–Zwanzig Operators

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

(2022) U. Fasel et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrast to VAR and DMD

(2021) Erik Bollt   CHAOS

Kernel-based prediction of non-Markovian time series

(2021) Faheem Gilani et al.   PHYSICA D-NONLINEAR PHENOMENA

Optimal renormalization of multiscale systems

(2021) Jacob Price et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

(2021) Yifeng Tian et al.   PHYSICS OF FLUIDS

Extracting and Modeling the Effects of Small-Scale Fluctuations on Large-Scale Fluctuations by Mori–Zwanzig Projection Operator Method

(2020) Shinya Maeyama et al.   JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

(2020) Elizabeth Qian et al.   PHYSICA D-NONLINEAR PHENOMENA

Machine Learning for Prediction with Missing Dynamics

(2020) John Harlim et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism

(2020) Kevin K. Lin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Renormalized Reduced Order Models with Memory for Long Time Prediction

(2019) Jacob Price et al.   MULTISCALE MODELING & SIMULATION

LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE

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

Some Recent Developments in Turbulence Closure Modeling

(2018) Paul A. Durbin   Annual Review of Fluid Mechanics

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

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

Deep learning for universal linear embeddings of nonlinear dynamics

(2018) Bethany Lusch et al.   Nature Communications

A dynamic subgrid scale model for Large Eddy Simulations based on the Mori–Zwanzig formalism

(2017) Eric J. Parish et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator

(2017) Hassan Arbabi et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism

(2017) Eric J. Parish et al.   Physical Review Fluids

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

Discrete approach to stochastic parametrization and dimension reduction in nonlinear dynamics

(2015) Alexandre J. Chorin et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial

(2012) Alvaro Nosedal-Sanchez et al.   AMERICAN STATISTICIAN

Dynamic mode decomposition of numerical and experimental data

(2010) PETER J. SCHMID   JOURNAL OF FLUID MECHANICS

Applications of the dynamic mode decomposition

(2010) P. J. Schmid et al.   THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS

Spectral analysis of nonlinear flows

(2009) CLARENCE W. ROWLEY et al.   JOURNAL OF FLUID MECHANICS

Computing generalized Langevin equations and generalized Fokker-Planck equations

(2009) E. Darve et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA