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：活动子空间（AS）方法为理解物理仿真输入与输出间关系提供了重要工具。本文提出了一种对传统AS方法的优雅推广，用于评估两个计算机模型的协同活动性。该推广方法——我们称之为协同活动子空间（C-AS）方法——支持对两个或多个计算机模型进行联合分析，从而深入探究各模型梯度空间的对齐（或非对齐）情况。我们定义了协同活动方向、协同敏感度指数以及标量“一致性”度量（及其互补的“非一致性”伪度量），并证明这些工具对于理解一类计算机模型的行为具有强大解释力，特别是在辅助传统AS分析时效果显著。本文提供了C-AS高效估计的具体方法，并配套发布了R软件包（github.com/knrumsey/concordance）。通过分析高能炸药PBX 9501的模拟速率棒实验数据集，展示了该方法在揭示复杂模型动力学特性方面的实际应用价值。