Anticipating tipping points and transitions via hybrid, analytic and data-informed, reduced systems

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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Photo by Annie Spratt on Unsplash

Photo by Annie Spratt on Unsplash

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