基于分层高斯过程的多保真地球系统建模的贝叶斯仿真
Bayesian Emulation of Multi-fidelity Earth System Modelling Using Hierarchical Gaussian Processes
- University of Exeter（埃克塞特大学）
- University of Greenwich（格林威治大学）
- Chinese Academy of Sciences（中国科学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文比较四种基于高斯过程的多保真仿真方法，在海啸和JULES模拟中评估性能，发现无单一方法普遍最优，选择需依保真度关系、高保真数据量和精度需求而定。
AI中文摘要：
多保真地球系统模型提供不同复杂程度和计算成本的模拟，但以最高保真度对参数空间进行穷尽探索通常代价高昂。多保真仿真器通过将丰富的低保真模拟与有限的高保真评估相结合，可以减轻这一负担。我们比较了四种基于高斯过程的多保真方法：Kennedy–O'Hagan自回归模型（K&O）、分层克里金（HK）、多级模型的贝叶斯分层仿真（BayHEm）以及多保真深度高斯过程（MF-DGP）。我们使用两个对比鲜明的应用来评估这些方法：一个三保真海啸模拟器和一个两保真的联合英国陆地环境模拟器（JULES）实现。性能通过留一法预测精度、不确定性表示、设计要求和计算特性进行评估。在海啸应用中，BayHEm给出了最低的归一化均方根误差（NRMSE = 0.031）和最高的SCORE（3.025），而MF-DGP在仅有10个高保真模拟可用时表现不如单保真基线。在JULES应用中，MF-DGP给出了最低的NRMSE（0.079）和最高的SCORE（3.032），所有30个留出的高保真观测值均位于其标称95%预测区间内。这些对比结果表明，没有单一的多保真仿真器是普遍优越的。相反，方法选择应反映保真度间关系的复杂性、可用高保真信息的数量以及对预测精度和不确定性量化的重视程度。
英文摘要：
Multi-fidelity Earth system models provide simulations at different levels of complexity and computational cost, but exhaustive exploration of the parameter space at the highest fidelity is often prohibitively expensive. Multi-fidelity emulators can reduce this burden by combining abundant lower-fidelity simulations with limited high-fidelity evaluations. We compare four Gaussian-process-based multi-fidelity approaches: the Kennedy--O'Hagan autoregressive model (K&O), hierarchical kriging (HK), Bayesian hierarchical emulation for multi-level models (BayHEm), and multi-fidelity deep Gaussian processes (MF-DGP). We evaluate the methods using two contrasting applications: a three-fidelity tsunami simulator and a two-fidelity implementation of the Joint UK Land Environment Simulator (JULES). Performance is assessed using leave-one-out predictive accuracy, uncertainty representation, design requirements, and computational characteristics. In the tsunami application, BayHEm gives the lowest normalised root mean square error (NRMSE = 0.031) and highest SCORE (3.025), while MF-DGP performs worse than the single-fidelity baseline when only 10 high-fidelity simulations are available. In the JULES application, MF-DGP gives the lowest NRMSE (0.079) and highest SCORE (3.032), with all 30 held-out high-fidelity observations lying within their nominal 95\% predictive intervals. These contrasting results show that no single multi-fidelity emulator is uniformly superior. Instead, method choice should reflect the complexity of the inter-fidelity relationship, the amount of high-fidelity information available, and the importance placed on predictive accuracy and uncertainty quantification.
