We consider an important problem in scientific discovery, namely identifying sparse governing equations for nonlinear dynamical systems. This involves solving sparse ridge regression problems to provable optimality in order to determine which terms drive the underlying dynamics. We propose a fast algorithm, OKRidge, for sparse ridge regression, using a novel lower bound calculation involving, first, a saddle point formulation, and from there, either solving (i) a linear system or (ii) using an ADMM-based approach, where the proximal operators can be efficiently evaluated by solving another linear system and an isotonic regression problem. We also propose a method to warm-start our solver, which leverages a beam search. Experimentally, our methods attain provable optimality with run times that are orders of magnitude faster than those of the existing MIP formulations solved by the commercial solver Gurobi.

翻译：本文考虑了科学发现中的一个重要问题，即识别非线性动力系统的稀疏控制方程。这涉及通过求解稀疏岭回归问题达到可证明的最优性，从而确定哪些项驱动了底层动力学。我们提出了一种快速算法OKRidge，用于稀疏岭回归，该算法采用一种新颖的下界计算方法：首先通过鞍点公式，进而求解（i）线性系统或（ii）采用基于ADMM的方法，其中近端算子可通过求解另一个线性系统和一个等渗回归问题进行高效计算。我们还提出了一种利用束搜索的求解器热启动方法。实验表明，我们的方法在运行时间上比现有由商业求解器Gurobi求解的MIP公式快数个数量级，同时实现了可证明的最优性。