Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks

Journal Article · 03 January 2025 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2024.117657 · OSTI ID:2502152

Zeng, Xiaoshu  ^[1]; Geraci, Gianluca ^[2]; Gorodetsky, Alex A. ^[3]; Jakeman, John D. ^[2]; Ghanem, Roger ^[1]

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1. Univ. of California, Los Angeles, CA (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
3. Univ. of Michigan, Ann Arbor, MI (United States)

The computational cost of high-fidelity numerical models makes outer-loop analysis, which requires repeated interrogation of the model such as uncertainty quantification, computationally demanding. Multi-fidelity methods, which construct a surrogate model using data from an ensemble of models of varying cost and accuracy, can substantially reduce the cost of outer-loop analysis. However, these methods can be difficult to apply when the model ensemble does not admit a clear hierarchy a priori and the correlations between models are low. Consequently, in this paper, we present a multi-fidelity method that leverages dimension reduction to enhance the correlation between models, thereby reducing the amount of data needed to train a surrogate from an unordered ensemble of models. Our method utilizes basis adaptation to build low-dimensional polynomial chaos expansions of each model and employs Multi-fidelity Networks to encode the relationships among models. We show that the resulting method exhibit two notable advantages over its counterpart: (1) enhanced accuracy (both reduced bias and variance); and (2) reduced dependency on the graph structure encoding relationships among models. We demonstrate the approach on an analytical test problem and a challenging finite element model for a spent nuclear fuel. Our method produces a surrogate model that is significantly more accurate than either a single-fidelity surrogate or a multi-fidelity surrogate constructed without basis adaptation.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); University of Southern California, Los Angeles, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003525; SC0021307
• OSTI ID: 2502152
• Report Number(s): SAND--2025-00436J
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: n/a Vol. 436; ISSN 0045-7825
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English