  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.
