{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:33:38Z","timestamp":1787340818400,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["FA9550-20-1-0358"],"award-info":[{"award-number":["FA9550-20-1-0358"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014036","name":"Multidisciplinary University Research Initiative","doi-asserted-by":"publisher","award":["FA9550-23-1-0671"],"award-info":[{"award-number":["FA9550-23-1-0671"]}],"id":[{"id":"10.13039\/100014036","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N0001422-1-2795"],"award-info":[{"award-number":["N0001422-1-2795"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0023191"],"award-info":[{"award-number":["DE-SC0023191"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Bayesian physics-informed neural networks serve as important scientific machine learning methods for uncertainty quantification. Although multilayer perceptrons are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov\u2013Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion with Chebyshev KANs. This gradient-free scheme effectively mitigates overfitting and enhances numerical stability. Additionally, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results demonstrate that the new method achieves comparable or better accuracy and much higher efficiency as well as stability compared to HMC, in addition to scalability.<\/jats:p>","DOI":"10.1137\/25m1729253","type":"journal-article","created":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T09:00:27Z","timestamp":1757926827000},"page":"1543-1577","source":"Crossref","is-referenced-by-count":4,"title":["Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks"],"prefix":"10.1137","volume":"13","author":[{"given":"Zhiwei","family":"Gao","sequence":"first","affiliation":[{"name":"Engineering, Brown University, Providence, RI 02906 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9713-7120","authenticated-orcid":true,"given":"George Em","family":"Karniadakis","sequence":"additional","affiliation":[{"name":"Corresponding author.\u00a0Division of Applied Mathematics, Brown University, Providence, RI 02912 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,9,15]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2025.129414"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0925-2312(93)90006-O"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"M. 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