We develop and test machine learning techniques for successfully using past state time series data and knowledge of a time-dependent system parameter to predict the evolution of the “climate” associated with the long-term behavior of a non-stationary dynamical system, where the non-stationary dynamical system is itself unknown. By the term climate, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term non-stationary, we refer to systems that are, themselves, varying with time. We show that our methods perform well on test systems predicting both continuous gradual climate evolution as well as relatively sudden climate changes (which we refer to as “regime transitions”). We consider not only noiseless (i.e., deterministic) non-stationary dynamical systems, but also climate prediction for non-stationary dynamical systems subject to stochastic forcing (i.e., dynamical noise), and we develop a method for handling this latter case. The main conclusion of this paper is that machine learning has great promise as a new and highly effective approach to accomplishing data driven prediction of non-stationary systems.
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March 2021
Research Article|
March 24 2021
Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity
Dhruvit Patel
;
Dhruvit Patel
a)
1
The Institute for Research in Electronics and Applied Physics, University of Maryland
, College Park, Maryland 26742, USA
a)Author to whom correspondence should be addressed: [email protected]
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Daniel Canaday;
Daniel Canaday
2Potomac Research LLC, Alexandria, Virginia 22311-1311,
USA
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Michelle Girvan;
Michelle Girvan
1
The Institute for Research in Electronics and Applied Physics, University of Maryland
, College Park, Maryland 26742, USA
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Andrew Pomerance;
Andrew Pomerance
2Potomac Research LLC, Alexandria, Virginia 22311-1311,
USA
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Edward Ott
Edward Ott
1
The Institute for Research in Electronics and Applied Physics, University of Maryland
, College Park, Maryland 26742, USA
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a)Author to whom correspondence should be addressed: [email protected]
Citation
Dhruvit Patel, Daniel Canaday, Michelle Girvan, Andrew Pomerance, Edward Ott; Using machine learning to predict statistical properties of non-stationary dynamical processes: System climate,regime transitions, and the effect of stochasticity. Chaos 1 March 2021; 31 (3): 033149. https://doi.org/10.1063/5.0042598
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