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.
New research published in the journal Chaos by Manuel Santos Gutiérrez and Valerio Lucarini, University of Reading, UK, Mickäel Chekroun, the Weizmann Institute, Israel and Michael Ghil, Ecole Normale Supérieure, Paris, France, showed using computer simulations that a machine learning programme called Empirical Model Reduction (EMR) in fact knows what it is doing.
To read the full press release visit https://www.reading.ac.uk/news-and-events/releases/PR856906.aspx
Full reference
M. Santos Gutiérrez, V. Lucarini, M. D. Chekroun, and M. Ghil , “Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator”, Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 053116 (2021) https://doi.org/10.1063/5.0039496
Abstract
Providing 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.
Parameterizations aim to reduce the complexity of high-dimensional dynamical systems. Here, a theory-based and a data-driven approach for the parameterization of coupled systems are compared, showing that both yield the same stochastic multilevel structure. The results provide very strong support to the use of empirical methods in model reduction and clarify the practical relevance of the proposed theoretical framework.
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