Conservative Surrogate Models for Optimization with the Active Subspace Method
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911258295402496 |
|---|---|
| author | Luneau, Philippe-André |
| author_facet | Luneau, Philippe-André |
| contents | We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of the full-size model, by making conservative approximations. The surrogate model is constructed using a Gaussian process regression (GPR). To ensure conservativeness, two new approaches are proposed: the first one using bootstrapping, and the second one using concentration inequalities. Those two techniques are based on a stochastic argument and thus will only enforce conservativeness up to a user-defined probability threshold. The method has applications in the context of optimization using the active subspace method for dimensionality reduction of the objective function and the constraints, addressing recorded issues about constraint violations. The resulting algorithms are tested on a toy optimization problem in thermal design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conservative Surrogate Models for Optimization with the Active Subspace Method Luneau, Philippe-André Numerical Analysis Optimization and Control 65K99, 65C20 We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of the full-size model, by making conservative approximations. The surrogate model is constructed using a Gaussian process regression (GPR). To ensure conservativeness, two new approaches are proposed: the first one using bootstrapping, and the second one using concentration inequalities. Those two techniques are based on a stochastic argument and thus will only enforce conservativeness up to a user-defined probability threshold. The method has applications in the context of optimization using the active subspace method for dimensionality reduction of the objective function and the constraints, addressing recorded issues about constraint violations. The resulting algorithms are tested on a toy optimization problem in thermal design. |
| title | Conservative Surrogate Models for Optimization with the Active Subspace Method |
| topic | Numerical Analysis Optimization and Control 65K99, 65C20 |
| url | https://arxiv.org/abs/2403.15678 |