Data-driven polynomial chaos expansion for machine learning regression

JOURNAL OF COMPUTATIONAL PHYSICS

卷:388

Article

Torre, Emiliano^1,2,3  Marelli, Stefano²  Embrechts, Paul^1,3,4  Sudret, Bruno^2,3 

[1] Swiss Fed Inst Technol, RiskLab, Zurich, Switzerland

[2] Swiss Fed Inst Technol, Chair Risk Safety & Uncertainty Quantificat, Zurich, Switzerland

[3] Swiss Fed Inst Technol, Risk Ctr, Zurich, Switzerland

[4] Swiss Fed Inst Technol, Swiss Finance Inst, Zurich, Switzerland

关键词: Polynomial chaos expansions;    Machine learning;    Regression;    Sparse representations;    Uncertainty quantification;    Copulas;   

DOI  :  10.1016/j.jcp.2019.03.039

来源: Elsevier

【 摘 要 】

We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive computational model subject to random inputs with an inexpensive-to-evaluate polynomial function. The metamodel obtained enables a reliable estimation of the statistics of the output, provided that a suitable probabilistic model of the input is available. Machine learning (ML) regression is a research field that focuses on providing purely data-driven input-output maps, with the focus on pointwise prediction accuracy. We show that a PCE metamodel purely trained on data can yield pointwise predictions whose accuracy is comparable to that of other ML regression models, such as neural networks and support vector machines. The comparisons are performed on benchmark datasets available from the literature. The methodology also enables the quantification of the output uncertainties, and is robust to noise. Furthermore, it enjoys additional desirable properties, such as good performance for small training sets and simplicity of construction, with only little parameter tuning required. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free