# Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models

arXiv: https://arxiv.org/abs/2311.18146 · HTML: https://mlsanity.com/paper/2311.18146/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2023.

## Built on by (most cited first, 4 of 4)

- [All Emulators are Wrong, Many are Useful, and Some are More Useful Than Others: A Reproducible Comparison of Computer Model Surrogates](https://mlsanity.com/paper/2512.09060/) (2025)
- [Active Subspaces in Infinite Dimension](https://mlsanity.com/paper/2510.11871/) (2025)
- [Bayesian Adaptive Polynomial Chaos Expansions](https://mlsanity.com/paper/2510.25036/) (2025)
- [Deep Intrinsic Coregionalization Multi-Output Gaussian Process Surrogate with Active Learning](https://mlsanity.com/paper/2508.16434/) (2025)

## Abstract (arXiv)

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.