Optimized sparse polynomial chaos expansion with entropy regularization

IF 2.9 3区 工程技术 Q2 ENGINEERING, MECHANICAL
SiJie Zeng, X. Duan, Jiangtao Chen, Liang Yan
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引用次数: 1

Abstract

Sparse Polynomial Chaos Expansion (PCE) is widely used in various engineering fields to quantitatively analyse the influence of uncertainty, while alleviating the problem of dimensionality curse. However, current sparse PCE techniques focus on choosing features with the largest coefficients, which may ignore uncertainties propagated with high order features. Hence, this paper proposes the idea of selecting polynomial chaos basis based on information entropy, which aims to retain the advantages of existing sparse techniques while considering entropy change as output uncertainty. A novel entropy-based optimization method is proposed to update the state-of-the-art sparse PCE models. This work further develops an entropy-based synthetic sparse model, which has higher computational efficiency. Two benchmark functions and a computational fluid dynamics (CFD) experiment are used to compare the accuracy and efficiency between the proposed method and classical methods. The results show that entropy-based methods can better capture the features of uncertainty propagation, improving accuracy and reducing sparsity while avoiding over-fitting problems.
熵正则化优化稀疏多项式混沌展开
稀疏多项式混沌展开(PCE)被广泛应用于各种工程领域,用于定量分析不确定性的影响,同时缓解维数诅咒问题。然而,当前的稀疏PCE技术专注于选择具有最大系数的特征,这可能会忽略高阶特征传播的不确定性。因此,本文提出了基于信息熵选择多项式混沌基的思想,旨在保留现有稀疏技术的优势,同时将熵的变化视为输出的不确定性。提出了一种新的基于熵的优化方法来更新现有的稀疏PCE模型。这项工作进一步发展了一个基于熵的合成稀疏模型,该模型具有更高的计算效率。使用两个基准函数和计算流体动力学(CFD)实验来比较所提出的方法与经典方法之间的准确性和效率。结果表明,基于熵的方法可以更好地捕捉不确定性传播的特征,在避免过拟合问题的同时提高精度和减少稀疏性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.50
自引率
4.30%
发文量
35
审稿时长
11 weeks
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