SINDyG：从图结构数据中稀疏识别非线性动力系统，应用于Stuart-Landau振荡器网络
SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with Applications to Stuart-Landau Oscillator Networks
AI总结：
本文提出SINDyG方法，通过整合网络结构到稀疏回归中，提升非线性动力系统建模的准确性和解释性，应用于神经元动力学研究。
摘要：
机器学习与稀疏促进技术的结合正在使直接从数据中提取支配方程成为可能，从而革新了科学和工程领域的计算建模。发现的动力学模型可用于应对气候科学、神经科学、生态学、金融、流行病学等领域的挑战。然而，大多数现有的稀疏识别方法在发现动力系统时将整个系统视为一个整体，而未考虑子系统的相互作用。为此，我们开发了一种新的方法，称为从图结构数据中稀疏识别非线性动力系统（SINDyG），该方法将网络结构整合到稀疏回归中，以识别解释底层网络动态的模型参数。我们通过几个神经动力学案例研究测试了所提出的方法，其中我们使用扩展的Stuart-Landau（SL）方程建模神经元群体的宏观振荡，并利用SINDyG方法识别底层非线性动态。我们的广泛计算实验验证了与原始SINDy方法相比，发现的网络动态在准确性和简洁性方面有所改进。所提出的图感知惩罚可以轻松集成到其他符号回归算法中，通过将网络结构整合到回归过程中，增强模型的可解释性和性能。
英文摘要：
The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered dynamical models could be used to address challenges in climate science, neuroscience, ecology, finance, epidemiology, and beyond. However, most existing sparse identification methods for discovering dynamical systems treat the whole system as one without considering the interactions between subsystems. As a result, such models are not able to capture small changes in the emergent system behavior. To address this issue, we developed a new method called Sparse Identification of Nonlinear Dynamical Systems from Graph-structured data (SINDyG), which incorporates the network structure into sparse regression to identify model parameters that explain the underlying network dynamics. We tested our proposed method using several case studies of neuronal dynamics, where we modeled the macroscopic oscillation of a population of neurons using the extended Stuart-Landau (SL) equation and utilize the SINDyG method to identify the underlying nonlinear dynamics. Our extensive computational experiments validate the improved accuracy and simplicity of discovered network dynamics when compared to the original SINDy approach. The proposed graph-informed penalty can be easily integrated with other symbolic regression algorithms, enhancing model interpretability and performance by incorporating network structure into the regression process.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
