Adaptive Gaussian Process Regression for Bayesian inverse problems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910428673605632 |
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| author | Villani, Paolo Unger, Jörg Weiser, Martin |
| author_facet | Villani, Paolo Unger, Jörg Weiser, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Gaussian Process Regression for Bayesian inverse problems Villani, Paolo Unger, Jörg Weiser, Martin Numerical Analysis 60G15, 62F15, 62F35, 65N21 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. |
| title | Adaptive Gaussian Process Regression for Bayesian inverse problems |
| topic | Numerical Analysis 60G15, 62F15, 62F35, 65N21 |
| url | https://arxiv.org/abs/2404.19459 |