基于稀疏回归和信息准则的动力系统模型选择
Model selection for dynamical systems via sparse regression and information criteria
摘要：
我们开发了一个算法模型选择，它允许考虑的组合大量的候选模型管理的动态系统。该创新避免了标准模型选择的缺点，标准模型选择通常由于计算信息标准的棘手性而限制了所考虑的候选模型的数量。使用最近开发的稀疏识别的非线性动力学算法，候选模型的Pareto边界附近的子选择允许一个易于处理的计算AIC（赤池信息标准）或BIC（贝叶斯信息标准）分数为其余的候选模型。信息标准对信息量最大的模型进行分级，从而能够自动和有原则地选择与时间序列数据相关的支持最强的模型。具体来说，我们表明AIC分数将每个候选模型置于{ \em强支持}、{ \em弱支持}或{ \em无支持}类别中。该方法正确地识别了几个典型的动力系统，包括SEIR（易感染-暴露-感染-恢复）疾病模型和洛伦兹方程，给出了正确的动力系统作为唯一的候选模型具有强有力的支持。
英文摘要：
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows for a tractable computation of AIC (Akaike information criteria) or BIC (Bayes information criteria) scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time series data. Specifically, we show that AIC scores place each candidate model in the {\em strong support}, {\em weak support} or {\em no support} category. The method correctly identifies several canonical dynamical systems, including an SEIR (susceptible-exposed-infectious-recovered) disease model and the Lorenz equations, giving the correct dynamical system as the only candidate model with strong support.
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