Active subspace (AS) methods are a valuable tool for understanding the relationship between the inputs and outputs of a Physics simulation. In this paper, an elegant generalization of the traditional ASM is developed to assess the co-activity of two computer models. This generalization, which we refer to as a Co-Active Subspace (C-AS) Method, allows for the joint analysis of two or more computer models allowing for thorough exploration of the alignment (or non-alignment) of the respective gradient spaces. We define co-active directions, co-sensitivity indices, and a scalar ``concordance" metric (and complementary ``discordance" pseudo-metric) and we demonstrate that these are powerful tools for understanding the behavior of a class of computer models, especially when used to supplement traditional AS analysis. Details for efficient estimation of the C-AS and an accompanying R package (github.com/knrumsey/concordance) are provided. Practical application is demonstrated through analyzing a set of simulated rate stick experiments for PBX 9501, a high explosive, offering insights into complex model dynamics.

翻译：活性子空间（Active Subspace, AS）方法是理解物理模拟输入与输出关系的重要工具。本文对传统活性子空间方法进行了优雅的泛化，以评估两个计算机模型的共活性。我们将这种泛化方法称为共活性子空间（C-AS）方法，它能够对两个或多个计算机模型进行联合分析，从而深入探索各自梯度空间的对齐（或非对齐）特性。我们定义了共活性方向、共敏感性指数以及标量"一致性"度量（及互补的"不一致性"伪度量），并证明这些工具是理解一类计算机模型行为的强大手段——尤其是当它们作为传统AS分析的补充时。本文还给出了C-AS的高效估计方法细节以及配套的R语言包（github.com/knrumsey/concordance）。通过分析PBX 9501（一种高能炸药）的模拟速率棒实验数据集，展示了该方法在实际应用中对复杂模型动力学的洞察能力。