Validation metric of multi-output model based on energy distance

Abstract

Abstract Model validation metrics have been developed to provide a quantitative measure that characterizes the agreement between predictions and observations. The validation metric of multi-output model has the problem of solving the joint probability density fuction (PDF). The traditional method is to reduce the dimension, but this may lead to the loss of some information. To avoid solving the joint PDF, this paper gives a validation metric method of multi-output model based on energy distance. At the same time, it avoids the problem of information loss caused by dimensionality reduction, and greatly reduces the difficulty of calculation. Then using mathematical examples, a set of numerical studies are designed to verify the correctness and stability of the method. Finally, we apply the metric to the Sandia validation challenge problem.