发表机构
University of Colorado Denver; Lawrence Livermore National Laboratory（科罗拉多大学丹佛分校; 劳伦斯利弗莫尔国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出结构化神经混沌（sNC）代理建模框架，结合PCE的可解释性与神经网络的表达能力，用于解决高维随机输入和功能响应系统的不确定性量化与全局敏感性分析问题，可自适应识别主导模式并低成本提取相关量。
AI 中文摘要
基于方差的全局敏感性分析（GSA）在不确定性量化中发挥关键作用，可识别不确定输入对模型响应变异性的贡献，但这些任务所需的重复模型评估往往成本过高；代理模型通过构建底层系统响应的低成本近似，提供了一种高效替代方案。构建兼具可扩展性和可解释性的代理模型以应对高维随机输入和功能响应的系统仍具挑战性，尤其是当需要跨空间或时间域的敏感性估计时。多项式混沌展开（PCE）因具有正交结构且与基于方差的敏感性度量直接相关，成为不确定性传播和敏感性分析的有效框架，但它存在维度灾难问题，对于具有功能响应的问题，计算负担会进一步放大。在本研究中，我们受PCE的可解释性和正交结构启发，提出结构化神经混沌（sNC）展开作为用于基于方差的GSA的代理建模框架。该框架保留了结构化分解的可解释性，同时利用了神经网络的表达能力；sNC展开镜像了截断的功能方差分析分解，其中每个交互分量允许可分离的低秩近似，其基函数和系数由神经网络参数化。该展开按顺序构建，自适应识别每个方差分析子空间内的主导模式，并确定表示的有效复杂度；所得结构能够以可忽略的成本直接从sNC展开的系数中提取统计和敏感性量。
英文摘要
Variance-based global sensitivity analysis (GSA) plays a key role in uncertainty quantification by identifying the contributions of uncertain inputs to the variability of the model response. The repeated model evaluations required for these tasks are often prohibitively expensive; surrogate models provide an efficient alternative by constructing inexpensive approximations of the underlying system response. Constructing surrogate models that combine scalability and interpretability for systems with high-dimensional stochastic inputs and functional responses remains challenging, particularly when sensitivity estimates are required across spatial or temporal domains. Polynomial chaos expansion (PCE) provides an effective framework for uncertainty propagation and sensitivity analysis due to its orthogonal structure and direct relationship with variance-based sensitivity measures. However, PCE suffers from the curse of dimensionality, whose computational burden is amplified for problems with functional responses. In this work, we introduce the Structured Neural Chaos (sNC) expansion as a surrogate modeling framework for variance-based GSA, inspired by the interpretability and orthogonal structure of PCE. The proposed framework retains the interpretability of structured decompositions while leveraging the expressive power of neural networks. The sNC expansion mirrors a truncated functional ANOVA decomposition, where each interaction component admits a separable low-rank approximation whose basis functions and coefficients are parameterized by neural networks. The expansion is constructed sequentially, adaptively identifying the dominant modes within each ANOVA subspace and determining the effective complexity of the representation. The resulting structure enables the extraction of statistical and sensitivity quantities directly from the coefficients of the sNC expansion at negligible cost.
Comments47 pages, 34 figures
