Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the potential to transform data-rich fields where well-established dynamical models remain unknown. This work contributes to the recent trend in data-driven sparse identification of nonlinear dynamics of finding the best sparse fit to observational data in a large library of potential nonlinear models. We propose an efficient first-order Conditional Gradient algorithm for solving the underlying optimization problem. In comparison to the most prominent alternative algorithms, the new algorithm shows significantly improved performance on several essential issues like sparsity-induction, structure-preservation, noise robustness, and sample efficiency. We demonstrate these advantages on several dynamics from the field of synchronization, particle dynamics, and enzyme chemistry.
翻译:管理方程式对于研究非线性动态至关重要,常常能够预测先前的不为人知的行为并将之纳入控制战略。因此,从数据中发现管理方程式有可能改变数据丰富的领域,而那些已建立已久的动态模型仍然不为人知。这项工作有助于数据驱动的非线性动态识别的最新趋势,即找到最适合潜在非线性模型大型图书馆中观测数据的最稀少的非线性动态。我们提出了解决潜在优化问题的高效第一阶条件梯级算法。与最突出的替代算法相比,新的算法显示,在诸如吸附、结构保护、噪声稳健性和样本效率等若干基本问题上的绩效显著提高。我们展示了同步、粒子动态和酶化学领域的若干动态的优势。