Evaluation of Surrogate Modeling as a Way to Reduce the Computational Burden of Numerical Simulations

摘要

Real-world application domains such as engineering design problems are computationally expensive. Some problems require thousands of simulations, which places a major burden on computing assets. Today's machine capacities have helped by affording users the ability to run numerous scenarios to discover a range of possible outcomes and to understand the influence of parameter variation on a problem. These activities become problematic as scenario sizes and complexities continuously increase. As a result, the high- performance computers often suffer at the hands of a combinatoric explosion. A single simulation may require hours to days to complete, and an exhaustive ('brute force') exploration of the design space for optimization purposes and 'what-if' analyses can easily call for thousands of simulations. An extreme example involves numerical simulations for a hurricane study for the Gulf of Mexico that was assigned approx. 4 million CPU hours per year over 3 years. This would require full utilization of over 500 CPUs. The effort proceeded in brute-force manner, exhaustively solving over an immense problem space, often with very minor tweaks to the initial conditions. This paper proposes a new approach to analyzing engineering design problems, replacing the numerical simulations with an emulation capability termed a surrogate model. Developing a surrogate model requires an accurate definition of the mapping between all of the interesting input values (i.e., the input space) and the associated output of the numerical simulation (i.e., the output space). The approach assumes that the number of simulations required to sufficiently cover this mapping is much smaller than assessing all possible conditions. A divide-and-conquer strategy (input bisection) is used to subdivide the input space (within an acceptable error bound), which leads to significant reductions in the number of simulations required.