In uncertainty quantification, variance-based global sensitivity analysis quantitatively determines the effect of each input random variable on the output by partitioning the total output variance into contributions from each input. However, computing conditional expectations can be prohibitively costly when working with expensive-to-evaluate models. Surrogate models can accelerate this, yet their accuracy depends on the quality and quantity of training data, which is expensive to generate (experimentally or computationally) for complex engineering systems. Thus, methods that work with limited data are desirable. We propose a diffeomorphic modulation under observable response preserving homotopy (D-MORPH) regression to train a polynomial dimensional decomposition surrogate of the output that minimizes the number of training data. The new method first computes a sparse Lasso solution and uses it to define the cost function. A subsequent D-MORPH regression minimizes the difference between the D-MORPH and Lasso solution. The resulting D-MORPH surrogate is more robust to input variations and more accurate with limited training data. We illustrate the accuracy and computational efficiency of the new surrogate for global sensitivity analysis using mathematical functions and an expensive-to-simulate model of char combustion. The new method is highly efficient, requiring only 15% of the training data compared to conventional regression.

翻译：在不确定性量化中，基于方差的全局敏感性分析通过将总输出方差分解为各输入变量的贡献，定量确定每个输入随机变量对输出的影响。然而，当处理计算代价高昂的模型时，计算条件期望的成本可能过高。代理模型可以加速这一过程，但其准确性取决于训练数据的质量和数量，而对于复杂工程系统，生成这些数据（通过实验或计算）代价高昂。因此，适用于有限数据的方法更具优势。我们提出一种基于可观测响应保持同伦的微分同胚调制（D-MORPH）回归方法，用于训练输出变量的多项式维度分解代理模型，从而最小化训练数据量。新方法首先计算稀疏Lasso解，并以此定义代价函数。随后通过D-MORPH回归最小化D-MORPH解与Lasso解之间的差异。得到的D-MORPH代理模型对输入变化具有更强的鲁棒性，且在有限训练数据下具有更高的准确性。我们通过数学函数及一个计算代价高昂的炭燃烧模拟模型，验证了新代理模型在全局敏感性分析中的精度与计算效率。与传统回归方法相比，新方法仅需15%的训练数据即能实现高效分析。