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.
Zeng, Xiaoshu, Geraci, Gianluca, Gorodetsky, Alex A., Jakeman, John D., & Ghanem, Roger (2025). Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks. Computer Methods in Applied Mechanics and Engineering, 436(n/a). https://doi.org/10.1016/j.cma.2024.117657
Zeng, Xiaoshu, Geraci, Gianluca, Gorodetsky, Alex A., et al., "Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks," Computer Methods in Applied Mechanics and Engineering 436, no. n/a (2025), https://doi.org/10.1016/j.cma.2024.117657
@article{osti_2502152,
author = {Zeng, Xiaoshu and Geraci, Gianluca and Gorodetsky, Alex A. and Jakeman, John D. and Ghanem, Roger},
title = {Boosting efficiency and reducing graph reliance: Basis adaptation integration in Bayesian multi-fidelity networks},
annote = {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.},
doi = {10.1016/j.cma.2024.117657},
url = {https://www.osti.gov/biblio/2502152},
journal = {Computer Methods in Applied Mechanics and Engineering},
issn = {ISSN 0045-7825},
number = {n/a},
volume = {436},
place = {United States},
publisher = {Elsevier},
year = {2025},
month = {01}}