The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing the conventional BIC to a set of overparameterized models derived from the potential regression models of different complexity measures. The result indicates that the asymptotic property of the UBIC and BIC holds indifferently.

翻译：不确定性惩罚信息准则（UBIC）已被提出作为数据驱动偏微分方程（PDE）发现的一种新模型选择准则。本文表明，使用UBIC等价于将传统BIC应用于一组源自不同复杂度度量潜在回归模型的过参数化模型。该结果表明，UBIC与BIC的渐近性质并无差异。