Sparse Bayesian learning for data driven polynomial chaos expansion with application to chemical processes

2018 ◽  
Vol 137 ◽  
pp. 553-565 ◽  
Author(s):  
Pham Luu Trung Duong ◽  
Le Quang Minh ◽  
Muhammad Abdul Qyyum ◽  
Moonyong Lee
Keyword(s):  
Bayesian Learning ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chemical Processes ◽  
Data Driven ◽  
Sparse Bayesian Learning ◽  
Chaos Expansion

A Sparse Data-Driven Polynomial Chaos Expansion Method for Uncertainty Propagation

2016 ◽  
Author(s):  
F. Wang ◽  
F. Xiong ◽  
S. Yang ◽  
Y. Xiong
Keyword(s):  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Data Driven ◽  
High Dimensional ◽  
Chaos Expansion ◽  
Least Angle Regression ◽  
Structure Problem

The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.

scholarly journals Data-driven polynomial chaos expansion for machine learning regression

2019 ◽  
Vol 388 ◽  
pp. 601-623 ◽  
Author(s):  
Emiliano Torre ◽  
Stefano Marelli ◽  
Paul Embrechts ◽  
Bruno Sudret
Keyword(s):  
Machine Learning ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Data Driven ◽  
Chaos Expansion
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