Artificial intelligence programmes used widely in climate science build an actual understanding of the climate system, meaning we can trust machine learning and further its applications in climate science, according to a new study.<\/p>\n
New research\u00a0published in the journal\u00a0Chaos<\/em><\/a>\u00a0by Manuel Santos Guti\u00e9rrez and Valerio Lucarini, University of Reading, UK, Mick\u00e4el Chekroun, the Weizmann Institute, Israel and Michael Ghil, Ecole Normale Sup\u00e9rieure, Paris, France, showed using computer simulations that a machine learning programme called Empirical Model Reduction (EMR) in fact knows what it is doing.<\/p>\n To read the full press release visit https:\/\/www.reading.ac.uk\/news-and-events\/releases\/PR856906.aspx<\/a><\/p>\n Full reference Abstract<\/strong>
\n<\/strong>M. Santos Guti\u00e9rrez, V. Lucarini, M. D. Chekroun, and M. Ghil , “Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator”,\u00a0Chaos: An Interdisciplinary Journal of Nonlinear Science<\/em>\u00a031, 053116 (2021)\u00a0https:\/\/doi.org\/10.1063\/5.0039496<\/a><\/p>\n
\nProviding efficient and accurate parameterizations for model reduction is a key goal in many areas of science and technology. Here, we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parameterizations of weakly coupled dynamical systems. Such parameterizations yield a set of stochastic integrodifferential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integrodifferential equations can be recast as a simpler multilevel Markovian model, and we establish an intuitive connection with a generalized Langevin equation. This connection helps setting up a parallelism between the top-down, equation-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings, on the one hand, support the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parameterizations.<\/p>\n