Document Zbl 1459.86011

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(2021)</a>. </div> <div class="abstract">Summary: 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 <span class="zbmathjax-textit">non-stationary</span> dynamical system, where the non-stationary dynamical system is itself unknown. By the term <span class="zbmathjax-textit">climate</span>, we mean the statistical properties of orbits rather than their precise trajectories in time. By the term <span class="zbmathjax-textit">non-stationary</span>, 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.<br class="zbmathjax-paragraph">©2021 American Institute of Physics</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7345198">Cited in <strong>8</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A86A08" title="MSC2020">86A08</a> </td> <td class="space"> Climate science and climate modeling </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A86-08" title="MSC2020">86-08</a> </td> <td class="space"> Computational methods for problems pertaining to geophysics </td> </tr></table> </div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1459.86011" data-ciurl="/ci/07345198" data-biburl="/bibtex/07345198.bib" data-amsurl="/amsrefs/07345198.bib" data-xmlurl="/xml/07345198.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07345198.pdf" title="Zbl 1459.86011 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1063/5.0042598" aria-label="DOI for “Using machine learning to predict statistical properties of non-stationary dynamical processes: system climate, regime transitions, and the effect of stochasticity”" title="10.1063/5.0042598">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Jaeger, H.; Haas, H., Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication, Science, 304, 78 (2004) · <a href="https://doi.org/10.1126/science.1091277" class="nowrap">doi:10.1126/science.1091277</a></td> </tr><tr> <td>[2]</td> <td class="space">Pathak, J.; Hunt, B. 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