arXiv Machine Learning October 23, 2026 By Jiaqiang Li, Jianbin Tan, Xueqin Wang

Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems

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Sparse Equation Matching (SEM) is a derivative‑free learning framework that uses integral‑based sparse regression with Green’s functions to discover differential operators and driving functions in general‑order dynamical systems. The method unifies several existing equation discovery techniques and is validated through extensive simulations that compare its performance to derivative‑based approaches. SEM is then applied to EEG data from 52 participants performing oculomotor tasks, successfully identifying active brain regions and task‑specific connectivity patterns.

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