不线性动力学与图书馆优化机制的稀疏识别:递归长期预测视角
IEEE transactions on cybernetics
|January 27, 2026
概括
本研究将SINDy与一个库优化机制 (SINDy-LOM) 介绍,用于自动设计基础函数库,用于发现动态系统方程. 与非线性动态的传统稀疏识别相比,SINDy-LOM提高了模型可靠性,并减少了用户的努力.
科学领域:
- 动态系统理论 动态系统理论
- 机器学习 机器学习
- 科学计算科学计算
背景情况:
- 非线性动态的稀疏识别 (SINDy) 是一种数据驱动的方法,用于发现治理方程.
- 在SINDy的一个关键挑战是手动设计候选基础函数库.
- 现有的SINDy方法往往只能保证前一步的预测准确度,从而限制了长期的可靠性.
研究的目的:
- 提出一种新的方法,SINDy与图书馆优化机制 (SINDy-LOM),以自动化图书馆设计.
- 通过递归长期 (RLT) 预测准确性来提高发现动态模型的可靠性.
- 为了减少与传统SINDy图书馆构建相关的用户负担.
主要方法:
- SINDy-LOM将稀疏回归与图书馆优化学习策略相结合.
- 采用双层优化架构:内部层用于模型提取,外部层用于基础函数优化.
- 基础函数是基于递归的长期预测准确性进行参数化和优化.
主要成果:
- SINDy-LOM成功地优化了基础函数库,减少了手工工作.
- 该方法产生了节,可解释和可用的闭式动态模型.
- 与传统SINDy的一步前进预测相比,RLT视角提高了模型可靠性.
结论:
- 在SINDy.LOM中,SINDy-LOM为自动化图书馆设计提供了一个有效的解决方案.
- 该方法提供了更可靠的动态模型,适合长期预测.
- 这种方法显著提高了数据驱动方程发现的可用性和适用性.
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