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Posterior sampling with Adaptive Gaussian Processes in Bayesian parameter identification

  • Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many more evaluations of the forward model. Replacing computationally expensive forward models by fast surrogate models is an attractive option. However, computing the simulated training data for building a sufficiently accurate surrogate model can be computationally expensive in itself, leading to the design of computer experiments problem of finding evaluation points and accuracies such that the highest accuracy is obtained given a fixed computational budget. Here, we consider a fully adaptive greedy approach to this problem. Using Gaussian process regression as surrogate, samples are drawn from the available posterior approximation while designs are incrementally defined by solving a sequence of optimization problems for evaluation accuracy andPosterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many more evaluations of the forward model. Replacing computationally expensive forward models by fast surrogate models is an attractive option. However, computing the simulated training data for building a sufficiently accurate surrogate model can be computationally expensive in itself, leading to the design of computer experiments problem of finding evaluation points and accuracies such that the highest accuracy is obtained given a fixed computational budget. Here, we consider a fully adaptive greedy approach to this problem. Using Gaussian process regression as surrogate, samples are drawn from the available posterior approximation while designs are incrementally defined by solving a sequence of optimization problems for evaluation accuracy and positions. The selection of training designs is tailored towards representing the posterior to be sampled as good as possible, while the interleaved sampling steps discard old inaccurate samples in favor of new, more accurate ones. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs.zeige mehrzeige weniger

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Metadaten
Autor*innen:P. Villani, Daniel Andés-Arcones, Jörg F. Unger, M. Weiser
Dokumenttyp:Preprint
Veröffentlichungsform:Graue Literatur
Sprache:Englisch
Titel des übergeordneten Werkes (Englisch):Numerical Analysis
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:23
DDC-Klassifikation:Technik, Medizin, angewandte Wissenschaften / Ingenieurwissenschaften / Ingenieurbau
Freie Schlagwörter:AGP; Adaptive Gaussian Processes; Bayesian parameter identification
Themenfelder/Aktivitätsfelder der BAM:Infrastruktur
Infrastruktur / Green Intelligent Building
DOI:10.48550/arXiv.2411.17858
URN:urn:nbn:de:kobv:b43-652731
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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