What is it about?
We introduce a framework for model reduction to produce analytic formulas to parameterize the neglected variables. These parameterizations are built from the original model’s equations in which only a scalar is left to calibrate per scale/variable to parameterize. This calibration is accomplished through a data-informed minimization of a least-square parameterization defect.
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Why is it important?
By their analytic fabric, the resulting parameterizations benefit physical interpretability. Furthermore, our hybrid framework—analytic and data-informed—enables us to bypass the so-called extrapolation problem, known to be an important issue for purely data-driven machine-learned parameterizations. Here, by training our parameterizations prior to transitions, we are able to perform accurate predictions of transitions such as tipping points via the corresponding reduced systems.
Perspectives
This work introduces an enticing and general framework that we are planning to deploy for the study of tipping elements occurring in complex systems
Mickael Chekroun
Weizmann Institute of Science
Read the Original
This page is a summary of: Optimal parameterizing manifolds for anticipating tipping points and higher-order critical transitions, Chaos An Interdisciplinary Journal of Nonlinear Science, September 2023, American Institute of Physics,
DOI: 10.1063/5.0167419.
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