A variance reduction method based on sensitivity derivatives

This paper establishes a general theoretical framework for variance reduction based on arbitrary order derivatives of the solution with respect to the random parameters, known as sensitivity derivatives. The theoretical results are validated by two examples—the solution of the Burgers equation with viscosity as a single random parameter, and a test case involving five random variables. These examples illustrate that the first-order sensitivity derivative variance reduction method achieves an order of magnitude improvement in accuracy for both Monte Carlo and stratified sampling schemes. The second-order sensitivity derivative method improves the accuracy by another order of magnitude relative to the first-order method. Coupling it with stratified sampling yields yet another order of magnitude improvement in accuracy.