Adversarial Dynamics and the Boundaries of Data-Driven Koopman Spectral Computability
When
Where
Speaker: Matthew Colbrook, University of Cambridge
Title: Adversarial Dynamics and the Boundaries of Data-Driven Koopman Spectral Computability
Abstract:
We classify the fundamental limits of data-driven Koopman spectral analysis, identifying which spectral quantities are computable and which remain impossible—even for randomized or adaptive algorithms. Central to this classification is the role of adversarial dynamics. Our framework reveals sharp boundaries: some spectral problems require three nested limits, while others admit finite-data algorithms with provable convergence guarantees. The space of observables emerges as a critical factor in determining what can be learned from data. We construct optimal algorithms in different settings and illustrate the impact of our results through applications such as sea ice forecasting, where robust spectral inference reveals coherent structures and long-term dynamics. This talk is part of a broader programme on infinite-dimensional spectral computations.