Global and local validation of computer experiments

Music City Center 

Computer simulations play a significant role in today's scientific discovery and engineering advancements. The validation of computer simulation models is a critical step in ensuring their reliability and accuracy before they are employed in practical applications. Effective validation not only builds confidence in the models' predictive capabilities but also identifies potential limitations and areas for improvement. This work focuses on statistical validation of computer models, with the goal of determining whether the computer response function differs from the physical process in a detectable manner. We formulate the validation process as a hypothesis testing problem: the computer model is invalidated if the null hypothesis is rejected. We introduce the local validation, which aims at identifying the subregions where the computer response and the physical process differ. Rigorous statistical methods are developed for global and local validation. The local tests are performed under a multiple testing framework.

Computer experiments

Uncertainty quantification

Multiple testing

Kernel ridge regression