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arXiv Machine Learning By Mark Kozdoba, Shie Mannor

Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems

Read the original on arXiv Machine Learning →

The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.

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