Title: Learning dynamical systems from data: When to tailor your nonlinear features?
Abstract:Â In the world of data-driven modeling of dynamical systems, some methods are more robust to the choice of nonlinear features than others. For example, the success of sparse identification of nonlinear dynamics (SINDy) depends crucially on a suitable nonlinear function library. In this regard, next-generation reservoir computing (NGRC) is generally considered more robust. In this talk, I will explore the role of nonlinear features in the machine learning of dynamical systems using SINDy and NGRC. First, I will show that NGRC can struggle in learning multistable dynamical systems when the provided nonlinearities do not match those in the ground-truth equations. Then, I will adapt SINDy to perform hypergraph inference from time-series data. Despite its commonly perceived fragility, our SINDy-based approach can perform model-free inference without tailoring nonlinear features. This allows us to reconstruct the effective connectivity in the brain from resting-state EEG data and demonstrate the importance of higher-order interactions in shaping macroscopic brain dynamics.
When:Â Mon, February 12, 2024 - 2:00pm
Where:Â 2136 PSC
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