增强与地球移动器距离和组相似性的非线性动态的稀疏识别
Donglin Liu1, Alexandros Sopasakis1
1Department of Mathematics, Lund University, 22362 Lund, Sweden.
Chaos (Woodbury, N.Y.)
|March 19, 2025
概括
组相似性SINDy (GS-SINDy) 增强了从数据中发现非线性动态. 这种方法通过整合稀疏性和相似性措施来提高准确性和稳定性,特别是在杂或低数据条件下.
科学领域:
- 动态系统理论 动态系统理论
- 计算科学 计算科学
- 数据驱动的建模数据驱动的建模
背景情况:
- 非线性动力学稀疏识别 (SINDy) 算法是从观测数据中发现治理方程的强大工具.
- 然而,在噪音的存在和有限的数据的情况下,SINDy的性能显著下降.
- 强有力的非线性动态的识别对于理解各种科学领域的复杂系统至关重要.
研究的目的:
- 开发一种先进的方法,提高非线性动态识别的稳定性和准确性.
- 提高学习由参数普通微分方程控制的动态系统函数的能力.
- 提高数据驱动模型在各种参数设置中的可解释性和适应性.
主要方法:
- 集团稀疏度值与地球移动器基于距离的相似度的整合.
- 组相似性SINDy (GS-SINDy) 算法的开发.
- 在基准动态系统上的应用和验证:Lotka-Volterra,Van der Pol,Lorenz和Brusselator模型.
主要成果:
- 与标准SINDy相比,GS-SINDy显示出明显提高了对噪声和低数据场景的稳定性.
- 该方法在识别非线性动态和学习系统函数方面实现了更高的准确性.
- GS-SINDy有效地隔离了不同数据集中的相关动态特征,提高了模型的适应性.
结论:
- GS-SINDy为数据驱动的非线性动态系统的发现提供了更可靠,更准确的方法.
- 增强的稳定性使其适用于现实世界的应用程序,其中数据质量可能会受到损害.
- 该方法通过提供更易于解释和适应的系统识别工具来推动科学机器学习领域的发展.
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