Probabilistic construction and numerical analysis of model verification and validation.

摘要

It the present manuscript, some recent developments in verification and validation (V&V) of predictive models are introduced. Verification is a mathematical concept which aims at assessing the accuracy of the solution of a given computational simulation compare to sufficiently accurate or analytical solutions. Validation, on the other hand, is a physics-based issue that aims at appraising the accuracy of a computational simulation compare to experimental data.; The proposed developments cast V&V in the form of an approximation-theoretic representation that permits their clear mathematical definition and resolution. In particular, three types of problems will be addressed. First, a priori and a posteriori error analysis of Wiener chaos spectral stochastic Galerkin scheme, a widely used tool for uncertainty propagation, are discussed. Second, a statistical procedure is developed in order to calibrate the uncertainty associated with parameters of a predictive model from experimental or model-based measurements. An important feature of such data-driven characterization algorithm, is in its ability to simultaneously represent both the intrinsic uncertainty and also the uncertainty due to data limitation. Third, a stochastic model reduction technique is proposed in order to increase the computational efficiency of spectral stochastic Galerkin schemes for the solution of complex stochastic systems.; While the second part of this research is essential in model validation phase, the first part is particularly important as it provides one with basic components of the verification phase.