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The concept of ``progressive Lattice Sampling`` as a basis for generating successive finite element response surfaces that are increasingly effective in matching actual response functions is investigated here. The goal is optimal response surface generation, which achieves an adequate representation of system behavior over the relevant parameter space of a problem with a minimum of computational and user effort. Such is important in global optimization and in estimation of system probabilistic response, which are both made much more viable by replacing large complex computer models of system behavior by fast running accurate approximations. This paper outlines the methodology for Finite Element/Lattice Sampling (FE/LS) response surface generation and examines the effectiveness of progressively refined FE/LS response surfaces in decoupled Monte Carlo analysis of several model problems. The proposed method is in all cases more efficient (generally orders of magnitude more efficient) than direct Monte Carlo evaluation, with no appreciable loss of accuracy. Thus, when arriving at probabilities or distributions by Monte Carlo, it appears to be more efficient to expend computer model function evaluations on building a FE/LS response surface than to expend them in direct Monte Carlo sampling. Furthermore, the marginal efficiency of the FE/LS decoupled Monte Carlo approach increases as the size of the computer model increases, which is a very favorable property.

Efficient Monte Carlo probability estimation with finite element response surfaces built from progressive lattice sampling