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Spectral Flow Learning Theory: Finite-Sample Guarantees for Vector-Field Identification
Chi Ho Leung, Philip E. Par\'e
https://arxiv.org/abs/2509.25000 https://

Spectral Flow Learning Theory: Finite-Sample Guarantees for Vector-Field Identification
We study the identification of continuous-time vector fields from irregularly sampled trajectories. We introduce Spectral Flow Learning (SFL), which learns in a windowed flow space using a lag-linear label operator that aggregates lagged Koopman actions. We provide finite-sample high-probability (FS-HP) guarantees for the class of variable-step linear multistep methods (vLLM). The FS-HP rates are constructed using spectral regularization with qualification-controlled filters for flow predictors…