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.

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