{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/stochastic-subspace-via-probabilistic","title":"Stochastic Subspace via Probabilistic Principal Component Analysis for Characterizing Model Error","arxiv_id":"2504.19963","date":"2025-04-28","proceeding":null,"authors":["Akash Yadav","Ruda Zhang"],"abstract":"This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities derived from the probabilistic PCA to construct distributions of the sample matrix, as well as the principal subspaces. It is applicable to projection-based reduced-order modeling methods, such as proper orthogonal decomposition and related model reduction methods. The stochastic subspace thus constructed can be used, for example, to characterize model-form uncertainty in computational mechanics. The proposed method has multiple desirable properties: (1) it is naturally justified by the probabilistic PCA and has analytic forms for the induced random matrix models; (2) it satisfies linear constraints, such as boundary conditions of all kinds, by default; (3) it has only one hyperparameter, which significantly simplifies training; and (4) its algorithm is very easy to implement. We demonstrate the performance of the proposed method via several numerical examples in computational mechanics and structural dynamics.","url_abs":"https://arxiv.org/abs/2504.19963v2","url_pdf":"https://arxiv.org/pdf/2504.19963v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"stochastic-subspace-via-probabilistic","repo_url":"https://github.com/UQUH/SS_PPCA","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}