Multi-Surrogate Modeling for Computational Cost Reduction

To utilize high-fidelity simulation for computationally intensive engineering applications such as sensitivity analysis and uncertainty quantification, the surrogate modeling techniques have become an indispensable tool and have been widely used. However, for reactor physics problems that can be characterized as very large number of input parameters (i.e. reaction cross sections), the required computational cost to build a surrogate model itself would be impractical with the sole conventional surrogate modeling techniques. We have been exploring the efficient way of reducing the computational cost in surrogate modeling and contributed the surrogate approach incorporated with reduced order modeling techniques. Basic approach summarized in Ref. is to transform the input parameters into low dimension by hybridizing two prominent methods - variational methods and sampling methods. As a preprocessing for the surrogate modeling, the influential subspace of the input parameters with respect to response change is extracted by range finding algorithm and the input parameters are projected onto that subspace. Because the number of subspace basis vectors are much smaller than the number of input parameters, reduced order form of the surrogate model can be constructed, which means that the number of unknowns to be determined in the surrogate modeling is reduced and, opposed to the curse of dimensionality, one can save significant computational cost to generate the training sample set. This study is the extension of the previous method for further cost reduction. In Ref., the input parameter transformation and the surrogate modeling are conducted independently. By doing that, one can estimate the error due to input parameter transformation and the surrogate modeling, separately and theoretically one can eliminate the error due to input parameter transformation within the machine precision. However, in practice, the input parameter variations, which may be considered significant in view of the input parameter transformation, may not be influential on the actual response change. By properly filtering those components, we expect that more reduction would be achieved. The basic idea and the preliminary test results are presented