弹性多保真贝叶斯模型校准

中文摘要 AI 辅助

函数型输出计算机模型的贝叶斯校准通常依赖于降维技术，如函数型主成分分析，这些技术假设模拟器实现之间的差异仅源于振幅变化。当模拟器输出还表现出相位变化（例如关键特征的时间或位置偏移）时，该假设被违反。近期工作通过弹性校准解决了这一问题，即在降维之前将函数型计算机模型实现与观测到的实验数据对齐。另外，多保真方法通过用少量昂贵的高保真模拟器运行补充大量廉价的低保真运行来降低校准成本。这通常通过映射策略（将低保真预测向高保真输出校正）或融合策略（在两个保真度之间构建共享基）来完成。本文结合了这两条研究路线，引入了弹性多保真贝叶斯模型校准，该方法在多保真映射或融合之前，将高保真和低保真函数型输出对齐到共同参考。在一个合成的二维校准问题和一个动态材料属性状态方程问题上，两种弹性多保真策略在留一法预测准确性上均匹配或优于单保真弹性仿真器，其中融合方法实现了最低误差。两种策略还产生了比单保真基线更紧的校准后验分布，其中融合方法提供了最佳覆盖率和最接近真实值的参数估计。

英文摘要

Bayesian calibration of functional-output computer models typically relies on dimension reduction techniques, such as functional principal component analysis, which assume that differences among simulator realizations arise only from amplitude variation. When simulator output also exhibits phase variation such as shifts in the timing or location of key features, this assumption is violated. Recent work has addressed this issue through elastic calibration, which aligns functional computer model realizations with observed experimental data prior to dimension reduction. Separately, multi-fidelity methods reduce the cost of calibration by supplementing a small number of expensive high-fidelity simulator runs with a larger ensemble of cheap low-fidelity runs. This is typically done through either a mapping strategy, which corrects low-fidelity predictions toward high-fidelity output, or a fusion strategy, which builds a shared basis across both fidelities. This paper combines these two lines of work, introducing elastic multi-fidelity Bayesian model calibration, which aligns high- and low-fidelity functional output to a common reference before applying multi-fidelity mapping or fusion. On a synthetic two-dimensional calibration problem and a dynamic material properties equation-of-state problem, both elastic multi-fidelity strategies match or improve on the leave-one-out predictive accuracy of a mono-fidelity elastic emulator, with the fusion approach achieving the lowest error. Both strategies also produce tighter calibrated posteriors than the mono-fidelity baseline, with the fusion approach providing the best coverage and parameter estimates closest to the true values.

发表机构

• Sandia National Laboratories（桑迪亚国家实验室）
• University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
• University of New Mexico（新墨西哥大学）

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