Calibration of Nested Computer Models

Abstract

Abstract. Thanks to computing power increase, risk quantification relies more and more on computer modelling. Methods of risk quantification based on a fixed computational budget exist, but computer models are almost always considered as a single black box.In this paper, we are interested in analyzing the behavior of a complex phenomenon, whose evolution can be modelled via two nested parametrized computer models. By two nested computer models, we mean that some inputs of the second model are outputs of the first model. Based on series of observations of the considered phenomenon, the idea is, first, to calibrate the parameters of each model, and then, to construct a predictor for the output of the second model, which takes into account the fact that, on the first hand, the two models are not perfect, and on the other hand, there exist uncertainties in the parameters' calibration.Concerning the calibration of the models' parameters we distinguish between the classic "black-box" method, parallel method and grouped method. In the case of a parallel calibration, each model is calibrated separately whereas in the case of a grouped calibration, the parameters of the two models are calibrated all together. In both cases, the extent to which the proposed predictor integrates the uncertainties of the nested system is demonstrated. The proposed methods are then applied to an example.