DOE OSTI2016
Reduced Order Modeling (ROM) is essential to enable the identification of the so-called active parameter subspace for high-fidelity models that are employed in computationally intensive analyses such as uncertainty characterization and data assimilation. Given the complexity of models for real-world application, brute force methods to identify the active subspace may not be computationally efficient to realize the value of reduction, since in realistic problems, the full scale model must be executed few hundred times, which may be computationally taxing. Earlier work has introduced a new approach, which represents a further development of our previous work on ROM, referred to as multi-level ROM (M-LROM). In M-LROM, approximate models are employed to identify the active subspace instead of the full scale model. In this summary, we present our recent results on M-LROM, specifically in regard to the construction of reliable error metrics that can bound the errors resulting from the reduction. The idea is to employ a lower fidelity model, i.e., an approximation of the full scale or high fidelity model, to build the active subspace, and via the proposed error bound, the quality of the active subspace can be determined by calculating an upper bound on the errors resulting from the reduction. For this approach to be practical, the error bound must be realistic, implying that it should be close to the actual errors expected, and not much higher. Therefore, an important goal of this summary is to compare different error bounds in terms of the relation between their estimated bounds to the actual errors. In particular, we compare the proposed error bound which numerically construct an estimator using binomial distribution to the widely used small-sample norm estimators. Unlike most probabilistic error estimation methods, the proposed bound employs a binomial distribution to construct the estimator whereas in other conventional methods, the distribution employed is typically the standard Gaussian, normalized over a unit hypersphere as initially proposed by the seminal paper of J. Dixon on random matrix theory. Previous publications provided evidence that the binomial distribution calculates more realistic bounds as compared to the Gaussian distribution, which tends to be conservative, implying that the bound is much bigger than the actual errors, which diminishes the value of the reduction, as now must increase the size of the active subspace to reach the desired upper bound on the reduction errors. This work has provided a rigorous approach by which error bounds on the reduction errors can be established without having to execute the high fidelity model during the construction of the active subspace. The high fidelity model is only need to test the error bound using small number of executions. This methodology paves the way for a more efficient application of ROM to complex engineering models, where standard ROM techniques may be too taxing to optimally realize their value in practical situations. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗