Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available

The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs each time they are run, even if the same input values are used. Stochastic computer models are more difficult to analyse and more difficult to emulate - often requiring substantially more computer model runs to fit. We present a method of using deterministic approximations of the computer model to better construct an emulator. The method is applied to numerous toy examples, as well as an idealistic epidemiology model, and a model from the building performance field

Global sensitivity analysis of computer models with functional inputs

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary meta-modeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The ``mean'' model allows to estimate the sensitivity indices of each scalar input variables, while the ``dispersion'' model allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation

Calibration and improved prediction of computer models by universal Kriging

This paper addresses the use of experimental data for calibrating a computer model and improving its predictions of the underlying physical system. A global statistical approach is proposed in which the bias between the computer model and the physical system is modeled as a realization of a Gaussian process. The application of classical statistical inference to this statistical model yields a rigorous method for calibrating the computer model and for adding to its predictions a statistical correction based on experimental data. This statistical correction can substantially improve the calibrated computer model for predicting the physical system on new experimental conditions. Furthermore, a quantification of the uncertainty of this prediction is provided. Physical expertise on the calibration parameters can also be taken into account in a Bayesian framework. Finally, the method is applied to the thermal-hydraulic code FLICA 4, in a single phase friction model framework. It allows to improve the predictions of the thermal-hydraulic code FLICA 4 significantly

Biomechanical Computer Models

In the past decade computer models have become very popular in the field of biomechanics due to exponentially increasing computer power. Biomechanical computer models can roughly be subdivided into two groups: multi-body models and numerical models. The theoretical aspects of both modelling strategies will be introduced. However, the focus of this chapter lies on demonstrating the power and versatility of computer models in the field of biomechanics by presenting sophisticated finite element models of human body parts. Special attention is paid to explain the setup of individual models using medical scan data. In order to reach the goal of individualising the model a chain of tools including medical imaging, image acquisition and processing, mesh generation, material modelling and finite element simulation –possibly on parallel computer architectures- becomes necessary. The basic concepts of these tools are described and application results are presented. The chapter ends with a short outlook into the future of computer biomechanics