Statistical Validation of Computer Models: Global and Subdomain Hypothesis Testing

2026-04-18

AI Summary

This study addresses the challenge of validating the consistency between computer models and real physical processes both globally and within local subregions. The authors propose a frequency-domain hypothesis testing framework that combines kernel ridge regression to estimate model discrepancy with weighted generalized Fourier coefficients for statistical inference. The key innovation is the Fourier Maximum Modulus Test (FMMT), which, for the first time, enables closed-form p-value computation with simultaneous sensitivity to both global and local deviations. Theoretical analysis establishes the asymptotic normality of the Fourier coefficients. Experimental results demonstrate that FMMT achieves high statistical power, accurate Type I error control, and strong sensitivity to localized discrepancies in both synthetic and shear-layer datasets.

Technology Category

• Machine Learning: Kernel Methods
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• Statistical Validation
• Computer Models
• Hypothesis Testing
• Model Discrepancy
• Subdomain Validation

Innovation

• Fourier Maximum Modulus Test
• kernel ridge regression
• statistical validation
• frequency-domain testing
• computer model discrepancy