Computer simulations play an important role in scientific discovery and engineering innovation. Reliable computer models enable virtual experimentation that reduces the need for costly and time-consuming physical testing. However, the credibility of such models hinges on rigorous statistical validation against real-world data. This paper develops a formal frequentist framework for both global and subdomain validation of computer models. We propose the Fourier Maximum Modulus Test (FMMT), which leverages kernel ridge regression (KRR) to estimate the discrepancy between the computer model and the physical process, followed by a frequency-domain test based on weighted generalized Fourier coefficients. The theoretical analysis establishes the asymptotic normality of these coefficients, allowing for closed-form p-values. Simulation studies and a shear-layer experiment demonstrate that FMMT achieves high power, accurate Type I error control, and strong sensitivity to localized discrepancies.

翻译：计算机模拟在科学发现和工程创新中发挥着重要作用。可靠的计算机模型使得虚拟实验成为可能，从而减少了对昂贵且耗时的物理测试的需求。然而，此类模型的可信度取决于基于真实世界数据的严格统计验证。本文提出了一种正式的频率论框架，用于计算机模型的全局与子域验证。我们提出了傅里叶最大模检验（FMMT），该方法利用核岭回归（KRR）估计计算机模型与物理过程之间的差异，随后基于加权广义傅里叶系数进行频域检验。理论分析确立了这些系数的渐近正态性，从而能够计算闭合形式的 p 值。模拟研究及剪切层实验表明，FMMT 实现了高检验功效、精确的第一类错误控制以及对局部差异的强敏感性。