Global sensitivity analysis with limited data via sparsity-promoting D-MORPH regression: Application to char combustion

TL;DR

This paper introduces a novel D-MORPH regression method that efficiently constructs surrogate models with limited data, enabling accurate global sensitivity analysis for complex, expensive simulations like char combustion.

Contribution

The paper presents a sparsity-promoting D-MORPH regression approach that reduces data requirements for surrogate modeling in global sensitivity analysis.

Findings

Requires only 15% of training data compared to traditional methods

Produces more robust and accurate surrogates with limited data

Demonstrates efficiency on complex char combustion model

Abstract

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 based 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.