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In uncertainty quantification, variance-based global sensitivity analysisquantitatively determines the effect of each input random variable on theoutput by partitioning the total output variance into contributions from eachinput. However, computing conditional expectations can be prohibitively costlywhen working with expensive-to-evaluate models. Surrogate models can acceleratethis, yet their accuracy depends on the quality and quantity of training data,which is expensive to generate (experimentally or computationally) for complexengineering systems. Thus, methods that work with limited data are desirable.We propose a diffeomorphic modulation under observable response preservinghomotopy (D-MORPH) regression to train a polynomial dimensional decompositionsurrogate of the output that minimizes the number of training data. The newmethod first computes a sparse Lasso solution and uses it to define the costfunction. A subsequent D-MORPH regression minimizes the difference between theD-MORPH and Lasso solution. The resulting D-MORPH surrogate is more robust toinput variations and more accurate with limited training data. We illustratethe accuracy and computational efficiency of the new surrogate for globalsensitivity analysis using mathematical functions and an expensive-to-simulatemodel of char combustion. The new method is highly efficient, requiring only15% of the training data compared to conventional regression.

Global sensitivity analysis in the limited data setting with application to char combustion