Surrogate modeling of high-dimensional problems via data-driven polynomial chaos expansions and sparse partial least square

For several years, studies conducted for discovering tenderness biomarkers have proposed a list of 20 candidates. The aim of the present work was to develop an innovative methodology to select the most predictive among this list. The relative abundance of the proteins was evaluated on five muscles of 10 Holstein cows: gluteobiceps, semimembranosus, semitendinosus, Triceps brachii and Vastus lateralis. To select the most predictive biomarkers, a multi-block model was used: The Data-Driven Sparse Partial Least Square. Semimembranosus and Vastus lateralis muscles tenderness could be well predicted (R2 = 0.95 and 0.94 respectively) with a total of 7 out of the 5 times 20 biomarkers analyzed. An original result is that the predictive proteins were the same for these two muscles: µ-calpain, m-calpain, h2afx and Hsp40 measured in m. gluteobiceps and µ-calpain, m-calpain and Hsp70-8 measured in m. Triceps brachii. Thus, this method is well adapted to this set of data, making it possible to propose robust candidate biomarkers of tenderness that need to be validated on a larger population.

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Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry

Reliability Engineering & System Safety ◽

10.1016/j.ress.2021.107923 ◽

2021 ◽

pp. 107923

Author(s):

Nabil El Moçayd ◽

Mohammed Seaid

Keyword(s):

Polynomial Chaos ◽

Data Driven ◽

Complex Fluid ◽

Polynomial Chaos Expansions ◽

Fluid Rheology

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

Volume 2A: 42nd Design Automation Conference ◽

10.1115/detc2016-59795 ◽

2016 ◽

Cited By ~ 1

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.

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