Publications

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Optimization is a key tool for scientific and engineering applications; however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational cost is proportional to the cost of performing a forward uncertainty analysis at each design location. An OUU workflow has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. In this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called multilevel Monte Carlo (MLMC) method, which is able to allocate resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our approach with respect to its Monte Carlo single fidelity counterpart.

Optimization is a key tool for scientific and engineering applications; however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational cost is proportional to the cost of performing a forward uncertainty analysis at each design location. An OUU workflow has two main components: an inner loop strategy for the computation of statistics of the quantity of interest, and an outer loop optimization strategy tasked with finding the optimal design, given a merit function based on the inner loop statistics. Here, in this work, we propose to alleviate the cost of the inner loop uncertainty analysis by leveraging the so-called multilevel Monte Carlo (MLMC) method, which is able to allocate resources over multiple models with varying accuracy and cost. The resource allocation problem in MLMC is formulated by minimizing the computational cost given a target variance for the estimator. We consider MLMC estimators for statistics usually employed in OUU workflows and solve the corresponding allocation problem. For the outer loop, we consider a derivative-free optimization strategy implemented in the SNOWPAC library; our novel strategy is implemented and released in the Dakota software toolkit. We discuss several numerical test cases to showcase the features and performance of our approach with respect to its Monte Carlo single fidelity counterpart.

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Spent nuclear fuel repository simulations are currently not able to incorporate detailed fuel matrix degradation (FMD) process models due to their computational cost, especially when large numbers of waste packages breach. The current paper uses machine learning to develop artificial neural network and k-nearest neighbor regression surrogate models that approximate the detailed FMD process model while being computationally much faster to evaluate. Using fuel cask temperature, dose rate, and the environmental concentrations of CO32−, O2, Fe2+, and H2 as inputs, these surrogates show good agreement with the FMD process model predictions of the UO2 degradation rate for conditions within the range of the training data. A demonstration in a full-scale shale repository reference case simulation shows that the incorporation of the surrogate models captures local and temporal environmental effects on fuel degradation rates while retaining good computational efficiency.

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This project created and demonstrated a framework for the efficient and accurate prediction of complex systems with only a limited amount of highly trusted data. These next generation computational multi-fidelity tools fuse multiple information sources of varying cost and accuracy to reduce the computational and experimental resources needed for designing and assessing complex multi-physics/scale/component systems. These tools have already been used to substantially improve the computational efficiency of simulation aided modeling activities from assessing thermal battery performance to predicting material deformation. This report summarizes the work carried out during a two year LDRD project. Specifically we present our technical accomplishments; project outputs such as publications, presentations and professional leadership activities; and the project’s legacy.

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The Spent Fuel and Waste Science and Technology (SFWST) Campaign of the U.S. Department of Energy (DOE) Office of Nuclear Energy (NE), Office of Spent Fuel & Waste Disposition (SFWD) is conducting research and development (R&D) on geologic disposal of spent nuclear fuel (SNF) and highlevel nuclear waste (HLW). A high priority for SFWST disposal R&D is disposal system modeling (DOE 2012, Table 6; Sevougian et al. 2019). The SFWST Geologic Disposal Safety Assessment (GDSA) work package is charged with developing a disposal system modeling and analysis capability for evaluating generic disposal system performance for nuclear waste in geologic media.

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