What can we learn about a dynamical system from data? – Impossibility results and classifications using adversarial dynamical systems

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• Matthew Colbrook (DAMTP)
• Monday 16 June 2025, 16:00-17:00
• Martin Ryle Seminar Room, KICC.

If you have a question about this talk, please contact Dr Priscilla Canizares.

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Machine learning has emerged as a powerful tool for studying complex nonlinear systems using trajectory data, with applications spanning climate science, epidemiology, and beyond. A fundamental question arises: When can we reliably learn system behaviours from data, and when is it fundamentally impossible? In this talk, I will introduce the concept of adversarial dynamical systems—systems specifically designed to prevent learning algorithms from converging. This approach enables the development of a rigorous classification framework that identifies the intrinsic difficulty of problems and establishes what is fundamentally unattainable. These results reveal impossibility theorems for data-driven system learning, showing that such adversarial systems arise with high probability and that reliable learning can remain out of reach regardless of the algorithm, data quality, or quantity. To illustrate, I will focus on Koopman operators, which reformulate nonlinear dynamics as infinite-dimensional spectral problems (search “Koopmania” for more!). By understanding these barriers, we can design methods that provably converge, achieving breakthroughs such as state-of-the-art predictions of Arctic sea ice dynamics. I would love to hear from those present whether these techniques could be useful in astrophysics too!

This talk is part of the Astro Data Science Discussion Group series.

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