Isabel Corona Guevara
University of Colorado Denver
Denver, CO
Data-driven surrogate modeling using sparse Bayesian machine learning with applications to uncertainty quantification
Isabel Corona
Polynomial chaos expansion (PCE) is a surrogate modeling approach which uses an orthogonal basis of polynomials to approximate a model response. Normally, the polynomials are chosen so that they are orthogonal with respect to the distribution of the input variables. Arbitrary polynomial chaos expansion (aPCE) is a similar surrogate-based approach which does not require knowledge of the probability density functions of the model inputs. Instead, the orthogonal polynomials are constructed purely based on the data. Our work aims to train the aPCE models with Bayesian learning techniques previously used on the classical PCE. This results in a sparse model where the number of terms in the aPCE is reduced significantly, ideally retaining only the most important terms. Additionally, we combine these sparse techniques with multi-element aPCE (ME-aPCE). ME-aPCE decomposes the input space into sub-domains in which an aPCE is then constructed locally in each sub-domain. We test the performance of the sparse aPCE models on three numerical examples; a classical toy example, the Ishigami function, a function modeling a cantilever tube structure and a function modeling an aircraft wing. The results show that the aPCE models perform as well as the classical PCE models and that the sparse models outperform their non-sparse counterparts. We also show that the ME-aPCE models can outperform the global models. Finally, we see that the sparse aPCE models can efficiently compute accurate sensitivity indices used for global sensitivity analysis.
SACNAS National Diversity in STEM Conference, Phoenix, AZ, October 30-November 2, 2024
