New perspectives for the prediction and statistical quantification of extreme events in high-dimensional dynamical systems

Data-assisted reduced-order modeling of extreme events in complex dynamical systems

(2018) Zhong Yi Wan et al.   PLoS One

Rogue waves and large deviations in deep sea

(2018) Giovanni Dematteis et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

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

Reduced-order prediction of rogue waves in two-dimensional deep-water waves

(2017) Mohammad Farazmand et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Extinction pathways and outbreak vulnerability in a stochastic Ebola model

(2017) Garrett T. Nieddu et al.   Journal of the Royal Society Interface

Extreme events and their optimal mitigation in nonlinear structural systems excited by stochastic loads: Application to ocean engineering systems

(2017) Han Kyul Joo et al.   OCEAN ENGINEERING

Reduced-space Gaussian Process Regression for data-driven probabilistic forecast of chaotic dynamical systems

(2017) Zhong Yi Wan et al.   PHYSICA D-NONLINEAR PHENOMENA

Chaos as an intermittently forced linear system

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

A variational approach to probing extreme events in turbulent dynamical systems

(2017) Mohammad Farazmand et al.   Science Advances

A probabilistic decomposition-synthesis method for the quantification of rare events due to internal instabilities

(2016) Mustafa A. Mohamad et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An adjoint-based approach for finding invariant solutions of Navier–Stokes equations

(2016) M. Farazmand   JOURNAL OF FLUID MECHANICS

Reduced-order precursors of rare events in unidirectional nonlinear water waves

(2016) Will Cousins et al.   JOURNAL OF FLUID MECHANICS

Probabilistic response and rare events in Mathieu׳s equation under correlated parametric excitation

(2016) Mustafa A. Mohamad et al.   OCEAN ENGINEERING

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 minimization principle for the description of modes associated with finite-time instabilities

(2016) H. Babaee et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Multiresolution Dynamic Mode Decomposition

(2016) J. Nathan Kutz et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Unsteady evolution of localized unidirectional deep-water wave groups

(2015) Will Cousins et al.   PHYSICAL REVIEW E

Probabilistic Description of Extreme Events in Intermittently Unstable Dynamical Systems Excited by Correlated Stochastic Processes

(2015) Mustafa A. Mohamad et al.   SIAM-ASA Journal on Uncertainty Quantification

Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model

(2014) Will Cousins et al.   PHYSICA D-NONLINEAR PHENOMENA

Attracting and repelling Lagrangian coherent structures from a single computation

(2013) Mohammad Farazmand et al.   CHAOS

Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow

(2013) Gary J. Chandler et al.   JOURNAL OF FLUID MECHANICS

Attractor local dimensionality, nonlinear energy transfers and finite-time instabilities in unstable dynamical systems with applications to two-dimensional fluid flows

(2013) T. P. Sapsis   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses

(2012) Kevin K. Chen et al.   JOURNAL OF NONLINEAR SCIENCE

Application of the dynamic mode decomposition to experimental data

(2011) Peter J. Schmid   EXPERIMENTS IN FLUIDS

Dynamic mode decomposition of numerical and experimental data

(2010) PETER J. SCHMID   JOURNAL OF FLUID MECHANICS

Enhanced vaccine control of epidemics in adaptive networks

(2010) Leah B. Shaw et al.   PHYSICAL REVIEW E

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

Dynamically orthogonal field equations for continuous stochastic dynamical systems

(2009) Themistoklis P. Sapsis et al.   PHYSICA D-NONLINEAR PHENOMENA

Large deviations

(2008) S. R. S. Varadhan   ANNALS OF PROBABILITY