Sequential adaptive design for emulating costly computer codes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916493271236608 |
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| author | Mohammadi, Hossein Challenor, Peter |
| author_facet | Mohammadi, Hossein Challenor, Peter |
| contents | Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of model evaluations remains challenging. We address this problem by suggesting a novel adaptive sampling criterion called VIGF (variance of improvement for global fit). The improvement function at any point is a measure of the deviation of the GP emulator from the nearest observed model output. At each iteration of the proposed algorithm, a new run is performed where VIGF is the largest. Then, the new sample is added to the design and the emulator is updated accordingly. A batch version of VIGF is also proposed which can save the user time when parallel computing is available. Additionally, VIGF is extended to the multi-fidelity case where the expensive high-fidelity model is predicted with the assistance of a lower fidelity simulator. This is performed via hierarchical kriging. The applicability of our method is assessed on a bunch of test functions and its performance is compared with several sequential sampling strategies. The results suggest that our method has a superior performance in predicting the benchmark functions in most cases. An implementation of VIGF is available in the dgpsi R package, which can be found on CRAN. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12113 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sequential adaptive design for emulating costly computer codes Mohammadi, Hossein Challenor, Peter Methodology Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of model evaluations remains challenging. We address this problem by suggesting a novel adaptive sampling criterion called VIGF (variance of improvement for global fit). The improvement function at any point is a measure of the deviation of the GP emulator from the nearest observed model output. At each iteration of the proposed algorithm, a new run is performed where VIGF is the largest. Then, the new sample is added to the design and the emulator is updated accordingly. A batch version of VIGF is also proposed which can save the user time when parallel computing is available. Additionally, VIGF is extended to the multi-fidelity case where the expensive high-fidelity model is predicted with the assistance of a lower fidelity simulator. This is performed via hierarchical kriging. The applicability of our method is assessed on a bunch of test functions and its performance is compared with several sequential sampling strategies. The results suggest that our method has a superior performance in predicting the benchmark functions in most cases. An implementation of VIGF is available in the dgpsi R package, which can be found on CRAN. |
| title | Sequential adaptive design for emulating costly computer codes |
| topic | Methodology |
| url | https://arxiv.org/abs/2206.12113 |