The ability of machine learning (ML) models to “extrapolate” to situations outside of the range spanned by their training data is crucial for predicting the long-term behavior of non-stationary dynamical systems (e.g., prediction of terrestrial climate change), since the future trajectories of such systems may (perhaps after crossing a tipping point) explore regions of state space which were not explored in past time-series measurements used as training data. We investigate the extent to which ML methods can yield useful results by extrapolation of such training data in the task of forecasting non-stationary dynamics, as well as conditions under which such methods fail. In general, we find that ML can be surprisingly effective even in situations that might appear to be extremely challenging, but do (as one would expect) fail when “too much” extrapolation is required. For the latter case, we show that good results can potentially be obtained by combining the ML approach with an available inaccurate conventional model based on scientific knowledge.
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Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems
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February 2023
Research Article|
February 27 2023
Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems

Dhruvit Patel
;
Dhruvit Patel
a)
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing)
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: dpp94@umd.edu
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Edward Ott
Edward Ott
(Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Writing – original draft, Writing – review & editing)
The Institute for Research in Electronics and Applied Physics, University of Maryland
, College Park, Maryland 26742, USA
Search for other works by this author on:
a)Author to whom correspondence should be addressed: dpp94@umd.edu
Note: This paper is part of the Focus Issue on Nonlinear dynamics, synchronization and networks: Dedicated to Juergen Kurths' 70th birthday.
Chaos 33, 023143 (2023)
Article history
Received:
October 24 2022
Accepted:
January 31 2023
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A companion article has been published:
Extrapolating dynamics with machine learning
Citation
Dhruvit Patel, Edward Ott; Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems. Chaos 1 February 2023; 33 (2): 023143. https://doi.org/10.1063/5.0131787
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