Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917728407781376 |
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| author | Rumsey, Kellin N. Hardy, Zachary K. Ahrens, Cory Wiel, Scott Vander |
| author_facet | Rumsey, Kellin N. Hardy, Zachary K. Ahrens, Cory Wiel, Scott Vander |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_18146 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models Rumsey, Kellin N. Hardy, Zachary K. Ahrens, Cory Wiel, Scott Vander Methodology 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. |
| title | Co-Active Subspace Methods for the Joint Analysis of Adjacent Computer Models |
| topic | Methodology |
| url | https://arxiv.org/abs/2311.18146 |