arXiv cs.LG + cs.RO + cs.HC· Jiaqiang Li, Jianbin Tan, Xueqin Wang·· 1 天前AI 评分38
Sparse Equation Matching：无需导数的通用阶动力系统学习框架
Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems
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研究者提出 Sparse Equation Matching（SEM），用基于格林函数的积分稀疏回归实现无需导数估计的通用阶动力系统方程发现，统一了多种现有方程发现方法。SEM 在仿真中与基于导数的方法做了基准对比，并应用于脑机接口实验中 52 名受试者执行多项眼动任务时记录的 EEG 数据，识别出跨受试者的活跃脑区与任务特异性连接模式。
正文 · 原文
Abstract:Equation discovery is a fundamental learning task for uncovering the underlying dynamics of complex systems, with wide-ranging applications in areas such as brain connectivity analysis, climate modeling, gene regulation, and physical simulation. However, many existing approaches rely on accurate derivative estimation and are limited to first-order dynamical systems, restricting their applicability in real-world scenarios. In this work, we propose Sparse Equation Matching (SEM), a unified framework that encompasses several existing equation discovery methods under a common formulation. SEM introduces an integral-based sparse regression approach using Green's functions, enabling derivative-free estimation of differential operators and their associated driving functions in general-order dynamical systems. The effectiveness of SEM is demonstrated through extensive simulations, benchmarking its performance against derivative-based approaches. We then apply SEM to electroencephalographic (EEG) data recorded during multiple oculomotor tasks, collected from 52 participants in a brain-computer interface experiment. Our method identifies active brain regions across participants and reveals task-specific connectivity patterns. These findings offer valuable insights into brain connectivity and the underlying neural mechanisms.
| Comments: | Accepted for publication in Statistics and Its Interface |
| Subjects: | Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2507.20072 [cs.LG] |
| (or arXiv:2507.20072v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2507.20072 arXiv-issued DOI via DataCite |
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| Related DOI: | https://doi.org/10.4310/SII.261008005403
DOI(s) linking to related resources |
Submission history
From: Jianbin Tan [view email]
[v1]
Sat, 26 Jul 2025 22:05:21 UTC (490 KB)
[v2]
Wed, 28 Jan 2026 01:28:51 UTC (527 KB)
[v3]
Wed, 21 Oct 2026 22:28:14 UTC (532 KB)
来源：arXiv cs.LG + cs.RO + cs.HC · arxiv.org