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Embedded Model Bias Quantification with Measurement Noise for Bayesian Model Calibration

  • A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. This paper introduces a more interpretable framework for embedding the model inadequacy compared to existing methods. To overcome the limitations of current approaches, we adapt the existing likelihood modelsA key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. Nevertheless, Bayesian methods paired with inexact models usually produce predictions unable to represent the observed datapoints. Additionally, the quantified uncertainties of these overconfident models cannot be propagated to other Quantities of Interest (QoIs) reliably. A promising solution involves embedding a model inadequacy term in the inference parameters, allowing the quantified model form uncertainty to influence non-observed QoIs. This paper introduces a more interpretable framework for embedding the model inadequacy compared to existing methods. To overcome the limitations of current approaches, we adapt the existing likelihood models to properly account for noise in the measurements and propose two new formulations designed to address their shortcomings. Moreover, we evaluate the performance of this inadequacy-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the model inadequacy term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction’s reliability. Finally, the proposed approach is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation using temperature observations.zeige mehrzeige weniger

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Metadaten
Autor*innen:Daniel Andrés Arcones, M. Weiser, P-S. Koutsourelakis, Jörg F. Unger
Dokumenttyp:Preprint
Veröffentlichungsform:Graue Literatur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Computational Engineering, Finance, and Science (cs.CE)
Jahr der Erstveröffentlichung:2025
Organisationseinheit der BAM:7 Bauwerkssicherheit
7 Bauwerkssicherheit / 7.7 Modellierung und Simulation
Veröffentlichende Institution:Bundesanstalt für Materialforschung und -prüfung (BAM)
Verlag:arXiv.org
Erste Seite:1
Letzte Seite:37
DDC-Klassifikation:Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurbau
Freie Schlagwörter:Bayesian inference; Model bias; Model updating; Noise; Quantity of Interest
Themenfelder/Aktivitätsfelder der BAM:Infrastruktur
Infrastruktur / Green Intelligent Building
DOI:10.48550/arXiv.2410.12037
URN:urn:nbn:de:kobv:b43-652720
Verfügbarkeit des Dokuments:Datei für die Öffentlichkeit verfügbar ("Open Access")
Lizenz (Deutsch):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
Datum der Freischaltung:05.01.2026
Referierte Publikation:Nein
Schriftenreihen ohne Nummerierung:Preprints der BAM
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