Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction
Machine learning’s integration into reliability analysis holds substantial potential to ensure infrastructure safety. Despite the merits of flexible tree structure and formulable expression, random forest (RF) and evolutionary polynomial regression (EPR) cannot contribute to reliability-based design...
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Cambridge University Press
2025-01-01
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| Series: | Data-Centric Engineering |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S263267362500005X/type/journal_article |
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| author | Geng-Fu He Pin Zhang Zhen-Yu Yin |
| author_facet | Geng-Fu He Pin Zhang Zhen-Yu Yin |
| author_sort | Geng-Fu He |
| collection | DOAJ |
| description | Machine learning’s integration into reliability analysis holds substantial potential to ensure infrastructure safety. Despite the merits of flexible tree structure and formulable expression, random forest (RF) and evolutionary polynomial regression (EPR) cannot contribute to reliability-based design due to absent uncertainty quantification (UQ), thus hampering broader applications. This study introduces quantile regression and variational inference (VI), tailored to RF and EPR for UQ, respectively, and explores their capability in identifying material indices. Specifically, quantile-based RF (QRF) quantifies uncertainty by weighting the distribution of observations in leaf nodes, while VI-based EPR (VIEPR) works by approximating the parametric posterior distribution of coefficients in polynomials. The compression index of clays is taken as an exemplar to develop models, which are compared in terms of accuracy and reliability, and also with deterministic counterparts. The results indicate that QRF outperforms VIEPR, exhibiting higher accuracy and confidence in UQ. In the regions of sparse data, predicted uncertainty becomes larger as errors increase, demonstrating the validity of UQ. The generalization ability of QRF is further verified on a new creep index database. The proposed uncertainty-incorporated modeling approaches are available under diverse preferences and possess significant prospects in broad scientific computing domains. |
| format | Article |
| id | doaj-art-73deddd4f7f941cba5a6352d62d96c01 |
| institution | DOAJ |
| issn | 2632-6736 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Data-Centric Engineering |
| spelling | doaj-art-73deddd4f7f941cba5a6352d62d96c012025-08-20T02:58:21ZengCambridge University PressData-Centric Engineering2632-67362025-01-01610.1017/dce.2025.5Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices predictionGeng-Fu He0https://orcid.org/0000-0002-6779-9676Pin Zhang1https://orcid.org/0000-0002-9004-647XZhen-Yu Yin2Department of Civil and Environmental Engineering, The Hong Kong, Polytechnic University, Hong Kong, ChinaDepartment of Engineering, University of Cambridge, Cambridge, UK Department of Civil and Environmental Engineering, National University of Singapore, SingaporeDepartment of Civil and Environmental Engineering, The Hong Kong, Polytechnic University, Hong Kong, ChinaMachine learning’s integration into reliability analysis holds substantial potential to ensure infrastructure safety. Despite the merits of flexible tree structure and formulable expression, random forest (RF) and evolutionary polynomial regression (EPR) cannot contribute to reliability-based design due to absent uncertainty quantification (UQ), thus hampering broader applications. This study introduces quantile regression and variational inference (VI), tailored to RF and EPR for UQ, respectively, and explores their capability in identifying material indices. Specifically, quantile-based RF (QRF) quantifies uncertainty by weighting the distribution of observations in leaf nodes, while VI-based EPR (VIEPR) works by approximating the parametric posterior distribution of coefficients in polynomials. The compression index of clays is taken as an exemplar to develop models, which are compared in terms of accuracy and reliability, and also with deterministic counterparts. The results indicate that QRF outperforms VIEPR, exhibiting higher accuracy and confidence in UQ. In the regions of sparse data, predicted uncertainty becomes larger as errors increase, demonstrating the validity of UQ. The generalization ability of QRF is further verified on a new creep index database. The proposed uncertainty-incorporated modeling approaches are available under diverse preferences and possess significant prospects in broad scientific computing domains.https://www.cambridge.org/core/product/identifier/S263267362500005X/type/journal_articleevolutionary polynomial regressionquantilerandom forestuncertainty quantificationvariational inference |
| spellingShingle | Geng-Fu He Pin Zhang Zhen-Yu Yin Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction Data-Centric Engineering evolutionary polynomial regression quantile random forest uncertainty quantification variational inference |
| title | Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction |
| title_full | Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction |
| title_fullStr | Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction |
| title_full_unstemmed | Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction |
| title_short | Uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction |
| title_sort | uncertainty quantification in tree structure and polynomial regression algorithms toward material indices prediction |
| topic | evolutionary polynomial regression quantile random forest uncertainty quantification variational inference |
| url | https://www.cambridge.org/core/product/identifier/S263267362500005X/type/journal_article |
| work_keys_str_mv | AT gengfuhe uncertaintyquantificationintreestructureandpolynomialregressionalgorithmstowardmaterialindicesprediction AT pinzhang uncertaintyquantificationintreestructureandpolynomialregressionalgorithmstowardmaterialindicesprediction AT zhenyuyin uncertaintyquantificationintreestructureandpolynomialregressionalgorithmstowardmaterialindicesprediction |