Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws

[2608.14840] Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2608.14840 (math) [Submitted on 14 Aug 2026 ( v1 ), last revised 2 Sep 2026 (this version, v2)] Title: Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws Authors: Jan Glaubitz , Daniel Sharp , Mathieu le Provost , Youssef M. Marzouk View a PDF of the paper titled Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws, by Jan Glaubitz and Daniel Sharp and Mathieu le Provost and Youssef M. Marzouk View PDF HTML (experimental) Abstract: We propose a novel regularity-informed filtering framework for data assimilation in the context of hyperbolic conservation laws and other time-dependent partial differential equations. We focus on systems whose states exhibit steep gradients and jump discontinuities. While filtering is widely used to improve numerical simulations by incorporating observational data, traditional filtering methods lack awareness of the spatial regularity of states produced in these systems. As a result, data assimilation often produces unphysical state estimates, introducing spurious oscillations in smooth regions and smearing sharp features. To address this limitation, we introduce a filtering framework that incorporates edge-preserving regularization into the filter's analysis step; this framework balances simulation forecasts, observational data, and structural prior knowledge. We formalize this approach using the ensemble Kalman filter (EnKF) and a class of hierarchical generalized sparse Bayesian learning (GSBL) priors, which adaptively infer spatially varying hyperparameters to promote non-oscillatory behavior in smooth regions while preserving discontinuities. We demonstrate the effectiveness of the resulting GSBL-EnKF method on challenging benchmark problems governed by hyperbolic conservation laws. Our results show that enforcing regularity in the analysis step yields sharper, less oscillatory state estimates and lower errors of the ensemble mean. This sometimes comes at the cost of ensemble spread, which we quantify and discuss. Subjects: Numerical Analysis (math.NA) ; Methodology (stat.ME) Cite as: arXiv:2608.14840 [math.NA] (or arXiv:2608.14840v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2608.14840 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Daniel Sharp [ view email ] [v1] Fri, 14 Aug 2026 19:25:14 UTC (18,685 KB) [v2] Wed, 2 Sep 2026 20:33:57 UTC (18,748 KB) Full-text links: Access Paper: View a PDF of the paper titled Regularity-informed data assimilation: A hierarchical Bayesian approach to ensemble Kalman filtering for hyperbolic conservation laws, by Jan Glaubitz and Daniel Sharp and Mathieu le Provost and Youssef M. Marzouk View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-08 Change to browse by: cs cs.NA math stat stat.ME References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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