Publications

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Surrogate construction is an essential component for all non-deterministic analyses in science and engineering. The efficient construction of easy and cheaper-to-run alternatives to a computationally expensive code paves the way for outer loop workflows for forward and inverse uncertainty quantification and optimization. Unfortunately, the accurate construction of a surrogate still remains a task that often requires a prohibitive number of computations, making the approach unattainable for large-scale and high-fidelity applications. Multifidelity approaches offer the possibility to lower the computational expense requirement on the highfidelity code by fusing data from additional sources. In this context, we have demonstrated that multifidelity Bayesian Networks (MFNets) can efficiently fuse information derived from models with an underlying complex dependency structure. In this contribution, we expand on our previous work by adopting a basis adaptation procedure for the selection of the linear model representing each data source. Our numerical results demonstrate that this procedure is computationally advantageous because it can maximize the use of limited data to learn and exploit the important structures shared among models. Two examples are considered to demonstrate the benefits of the proposed approach: an analytical problem and a nuclear fuel finite element assembly. From these two applications, a lower dependency of MFnets on the model graph has been also observed.

We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. Besides requiring significantly less trainable parameters than equivalent fully connected networks, encoder, decoder, encoder-decoder or decoder-encoder architectures can learn the mapping between inputs to outputs of arbitrary dimensionality. We demonstrate their accuracy when trained on a few high-fidelity and many low-fidelity data generated from models ranging from one-dimensional functions to Poisson equation solvers in two-dimensions. We finally discuss a number of implementation choices that improve the reliability of the uncertainty estimates generated by Monte Carlo DropBlocks, and compare uncertainty estimates among low-, high- and multifidelity approaches.

We analyze the regression accuracy of convolutional neural networks assembled from encoders, decoders and skip connections and trained with multifidelity data. Besides requiring significantly less trainable parameters than equivalent fully connected networks, encoder, decoder, encoder-decoder or decoder-encoder architectures can learn the mapping between inputs to outputs of arbitrary dimensionality. We demonstrate their accuracy when trained on a few high-fidelity and many low-fidelity data generated from models ranging from one-dimensional functions to Poisson equation solvers in two-dimensions. We finally discuss a number of implementation choices that improve the reliability of the uncertainty estimates generated by Monte Carlo DropBlocks, and compare uncertainty estimates among low-, high- and multifidelity approaches.

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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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This report documents the results of an FY22 ASC V&V level 2 milestone demonstrating new algorithms for multifidelity uncertainty quantification. Part I of the report describes the algorithms, studies their performance on a simple model problem, and then deploys the methods to a thermal battery example from the open literature. Part II (restricted distribution) applies the multifidelity UQ methods to specific thermal batteries of interest to the NNSA/ASC program.

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