用降温机制优化稀疏模型发现，提升物理方程提取准确率
Optimizing Hard Thresholding for Sparse Model Discovery
- 引入降温策略重激活被剔除的项，改进硬阈值方法
- 在多个非线性系统中，模型精度显著提升
- 适合需要可解释物理模型的科研人员使用
许多模型选择算法依赖稀疏字典学习来获取可解释且基于物理的控制方程。优化算法通常通过硬阈值过程移除无关库项以强制系数稀疏。本文提出一种退火机制，按冷却计划重新激活部分被移除项，从而提升稀疏学习算法性能。聚焦两种优化方法：SINDy 和基于硬阈值追逐的替代方案。在对对流流动、激发系统和种群动力学等多类非线性系统的对比实验中，退火均有效提升了模型准确性。最后，该方法应用于弹道运动的实验数据，验证了其实际有效性。
原文摘要 · Abstract (English)
Many model selection algorithms rely on sparse dictionary learning to provide interpretable and physics-based governing equations. The optimization algorithms typically use a hard thresholding process to enforce sparse activations in the model coefficients by removing library elements from consideration. By introducing an annealing scheme that reactivates a fraction of the removed terms with a cooling schedule, we are able to improve the performance of these sparse learning algorithms. We concentrate on two approaches to the optimization, SINDy, and an alternative using hard thresholding pursuit. We see in both cases that annealing can improve model accuracy. The effectiveness of annealing is demonstrated through comparisons on several nonlinear systems pulled from convective flows, excitable systems, and population dynamics. Finally we apply these algorithms to experimental data for projectile motion.
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