Adaptive Gaussian Process Regression for Bayesian inverse problems Article Swipe
Paolo Villani
,
Jörg F. Unger
,
Martin Weiser
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2404.19459
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2404.19459
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on optimizing both the positioning and simulation accuracy of training data in order to reduce the computational cost of simulating training data without compromising the fidelity of the posterior distributions of parameters. The method interleaves a goal-oriented active learning algorithm selecting evaluation points and tolerances based on the expected impact on the Kullback-Leibler divergence of surrogated and true posterior with a Markov Chain Monte Carlo sampling of the posterior. The performance benefit of the adaptive approach is demonstrated for two simple test problems.
Related Topics
Concepts
Bayesian probability
Gaussian process
Inverse Gaussian distribution
Regression
Kriging
Bayesian linear regression
Econometrics
Inverse
Computer science
Process (computing)
Mathematics
Gaussian
Statistics
Applied mathematics
Artificial intelligence
Machine learning
Bayesian inference
Physics
Mathematical analysis
Distribution (mathematics)
Operating system
Quantum mechanics
Geometry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2404.19459
- https://arxiv.org/pdf/2404.19459
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4396600718
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4396600718Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2404.19459Digital Object Identifier
- Title
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Adaptive Gaussian Process Regression for Bayesian inverse problemsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-04-30Full publication date if available
- Authors
-
Paolo Villani, Jörg F. Unger, Martin WeiserList of authors in order
- Landing page
-
https://arxiv.org/abs/2404.19459Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2404.19459Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2404.19459Direct OA link when available
- Concepts
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Bayesian probability, Gaussian process, Inverse Gaussian distribution, Regression, Kriging, Bayesian linear regression, Econometrics, Inverse, Computer science, Process (computing), Mathematics, Gaussian, Statistics, Applied mathematics, Artificial intelligence, Machine learning, Bayesian inference, Physics, Mathematical analysis, Distribution (mathematics), Operating system, Quantum mechanics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.goal-oriented | 66 |
| abstract_inverted_index.Kullback-Leibler | 82 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |