论文标题
通过混合构成优化学习稀疏的非线性动力学
Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimization
论文作者
论文摘要
直接从数据中发现复杂动力学系统的管理方程是科学机器学习中的一个核心问题。近年来，由启发式稀疏回归方法驱动的非线性动力学（Sindy）框架的稀疏识别已成为学习简约模型的主要工具。我们建议使用混合智能优化（MIO）对Sindy问题进行确切的表述，以在几秒钟内解决稀疏性的限制回归问题，以证明最优性。在大量规范的普通和部分微分方程上，我们说明了准确模型发现中方法的显着改善，同时更有效，噪声稳健，并且在适应物理约束方面具有灵活性。
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic sparse regression methods, has become a dominant tool for learning parsimonious models. We propose an exact formulation of the SINDy problem using mixed-integer optimization (MIO) to solve the sparsity constrained regression problem to provable optimality in seconds. On a large number of canonical ordinary and partial differential equations, we illustrate the dramatic improvement of our approach in accurate model discovery while being more sample efficient, robust to noise, and flexible in accommodating physical constraints.
