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1 code implementation • 9 Nov 2022 • Alexander Wikner, Joseph Harvey, Michelle Girvan, Brian R. Hunt, Andrew Pomerance, Thomas Antonsen, Edward Ott

In this article, we systematically examine the technique of adding noise to the ML model input during training to promote stability and improve prediction accuracy.

no code implementations • 1 Jul 2022 • Dhruvit Patel, Edward Ott

We focus on the particularly challenging situation where the past dynamical state time series that is available for ML training predominantly lies in a restricted region of the state space, while the behavior to be predicted evolves on a larger state space set not fully observed by the ML model during training.

no code implementations • 13 Apr 2022 • Shukai Ma, Thomas M. Antonsen, Steven M. Anlage, Edward Ott

Machine learning (ML) has found widespread application over a broad range of important tasks.

no code implementations • 27 Aug 2021 • Keshav Srinivasan, Nolan Coble, Joy Hamlin, Thomas Antonsen, Edward Ott, Michelle Girvan

Forecasting the dynamics of large complex networks from previous time-series data is important in a wide range of contexts.

no code implementations • 15 Feb 2021 • Alexander Wikner, Jaideep Pathak, Brian R. Hunt, Istvan Szunyogh, Michelle Girvan, Edward Ott

We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.

no code implementations • 29 Oct 2020 • Amitava Banerjee, Joseph D. Hart, Rajarshi Roy, Edward Ott

To achieve this, we first train a type of machine learning system known as reservoir computing to mimic the dynamics of the unknown network.

no code implementations • 10 Feb 2020 • Alexander Wikner, Jaideep Pathak, Brian Hunt, Michelle Girvan, Troy Arcomano, Istvan Szunyogh, Andrew Pomerance, Edward Ott

We consider the commonly encountered situation (e. g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics.

no code implementations • 5 Dec 2019 • Amitava Banerjee, Jaideep Pathak, Rajarshi Roy, Juan G. Restrepo, Edward Ott

Our technique leverages the results of a machine learning process for short time prediction to achieve our goal.

1 code implementation • 18 Oct 2019 • Sanjukta Krishnagopal, Michelle Girvan, Edward Ott, Brian Hunt

Indeed, our method works well when the component frequency spectra are indistinguishable - a case where a Wiener filter performs essentially no separation.

1 code implementation • 9 Oct 2019 • Pantelis R. Vlachas, Jaideep Pathak, Brian R. Hunt, Themistoklis P. Sapsis, Michelle Girvan, Edward Ott, Petros Koumoutsakos

We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal dynamics of high dimensional and reduced order complex systems using Reservoir Computing (RC) and Backpropagation through time (BPTT) for gated network architectures.

no code implementations • 9 Mar 2018 • Jaideep Pathak, Alexander Wikner, Rebeckah Fussell, Sarthak Chandra, Brian Hunt, Michelle Girvan, Edward Ott

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system.

no code implementations • 19 Oct 2017 • Jaideep Pathak, Zhixin Lu, Brian R. Hunt, Michelle Girvan, Edward Ott

For the case of the KS equation, we note that as the system's spatial size is increased, the number of Lyapunov exponents increases, thus yielding a challenging test of our method, which we find the method successfully passes.

Chaotic Dynamics

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