论文标题
sindy-pi：一种可行的算法，用于平行隐式的非线性动力学稀疏识别
SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics
论文作者
论文摘要
通过测量数据准确地对系统的非线性动力学进行建模是一个具有挑战性但至关重要的话题。非线性动力学（SINDY）算法的稀疏识别是从数据发现动态系统模型的一种方法。尽管已经开发了扩展来识别由理性函数描述的隐式动态或动力学，但这些扩展对噪声非常敏感。在这项工作中，我们开发了sindy-pi（并行，隐式），这是信德算法的强大变体，以识别隐式动态和理性的非线性。 Sindy-Pi框架包括多种优化算法和模型选择的原则方法。我们证明了该算法从有限和嘈杂的数据中学习隐性的普通和部分微分方程和保护定律的能力。特别是，我们表明所提出的方法是比以前的方法更强的噪声数量，可以用来识别一类复杂的ODE和PDE动力学，这些动力和PDE动力学以前与Sindy无法实现的动力学，包括双摆动力学以及Belousov Zhabotinskinsky（BZ）的反应。
Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of complex ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and the Belousov Zhabotinsky (BZ) reaction.
