Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance

[2601.16425] Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance Skip to main content Search Submit Donate Log in Computer Science > Machine Learning arXiv:2601.16425 (cs) [Submitted on 23 Jan 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Bayesian Experimental Design for Model Discrepancy Calibration: A Rivalry between Kullback--Leibler Divergence and Wasserstein Distance Authors: Huchen Yang , Xinghao Dong , Jin-Long Wu View PDF HTML (experimental) Abstract: Designing experiments that systematically gather data from complex physical systems is central to accelerating scientific discovery. While Bayesian experimental design (BED) provides a principled, information-based framework that integrates experimental planning with probabilistic inference, the selection of utility functions in BED is a long-standing and active topic, where different criteria emphasize different notions of information. Although Kullback--Leibler (KL) divergence has been one of the most common choices, recent studies have proposed Wasserstein distance as an alternative. In this work, we first employ a toy example to illustrate an issue of Wasserstein distance - the value of Wasserstein distance of a fixed-shape posterior depends on the relative position of its main mass within the support and can exhibit false rewards unrelated to information gain, especially with a non-informative prior (e.g., uniform distribution). We then further provide a systematic comparison between these two criteria through a classical source inversion problem in the BED literature, revealing that the KL divergence tends to lead to faster convergence in the absence of model discrepancy, while Wasserstein metrics provide more robust sequential BED results if model discrepancy is non-negligible. These findings clarify the trade-offs between KL divergence and Wasserstein metrics for the utility function and provide guidelines for selecting suitable criteria in practical BED applications. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2601.16425 [cs.LG] (or arXiv:2601.16425v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2601.16425 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Computational Physics 545 (2026) 114469 Related DOI : https://doi.org/10.1016/j.jcp.2025.114469 Focus to learn more DOI(s) linking to related resources Submission history From: Huchen Yang [ view email ] [v1] Fri, 23 Jan 2026 03:34:10 UTC (7,642 KB) [v2] Fri, 28 Aug 2026 00:48:16 UTC (9,187 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG < prev | next > new | recent | 2026-01 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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