面向含噪模拟器输出的多输出正交高斯过程
Multi-output Orthogonal Gaussian Processes for Noisy Simulator Outputs
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中文总结 AI 辅助
针对含噪模拟器输出的建模难题，提出多输出正交高斯过程MOOGP，通过定义正交性、构造协方差函数及结构化似然，在趋势恢复、数值实验与重离子碰撞模拟中展现出可解释性与预测优势。
中文摘要 AI 辅助
计算机模拟可对物理过程建模，但通常运行成本过高，难以生成足够的运行次数用于校准、敏感性分析、预测及不确定性量化。因此，统计代理模型常被用作更经济的替代方案，可基于少量模拟运行进行训练。高斯过程（GP）非常适合作为代理模型，因其能提供灵活的非线性回归及闭式不确定性量化。然而，标准GP无法胜任更复杂模拟器的替代任务，例如随机或多输出模拟器。此外，典型GP还难以将拟合的回归系数与残差过程变异分离。我们提出多输出正交高斯过程（MOOGP）以解决上述问题。本文有三项主要贡献：（i）定义多输出高斯过程的正交性；（ii）通过对每个协方差函数进行条件化来强制正交性的构造方法；（iii）可显著提升计算扩展性的结构化似然公式。在趋势恢复示例中，MOOGP能恢复真实趋势，而非正交化的对应模型则无法做到，甚至会反转趋势符号。数值实验及在重离子碰撞模拟中的应用进一步证明了MOOGP的可解释性与预测优势。
英文摘要
Computer simulations can model physical processes but are often too expensive to produce enough runs for calibration, sensitivity analysis, prediction, and uncertainty quantification. As a result, statistical surrogates are frequently used as cheaper alternatives that can be trained on a small number of simulation runs. Gaussian processes (GP) are well-suited as surrogates, as they provide flexible, nonlinear regression and closed-form uncertainty quantification. However, standard GPs are insufficient replacements for more complex simulators, such as stochastic or multi-output simulators. In addition, typical GPs also struggle to separate fitted regression coefficients from residual process variation. We introduce multi-output orthogonal Gaussian process (MOOGP) to tackle the problems mentioned above. This paper has three main contributions: (i) a definition of orthogonality for multi-output Gaussian processes, (ii) a construction that enforces orthogonality by conditioning each covariance function, and (iii) a structured likelihood formulation that significantly improves computational scaling. In a trend-recovery illustrative example, MOOGP recovers the true trend while the non-orthogonalized counterpart fails to do so, to the extent it reverses the sign of the trend. Numerical experiments and an application in heavy-ion collision simulations further demonstrate the interpretability and predictive advantage of MOOGP.
