Inverse uncertainty quantification of a distributed parameter system: An application for glass forming model

摘要

Mathematically, many non-trivial processes involving thermal or fluid transfer can be described as distributed parameter systems. The evolution of a system is governed by partial differential equations (PDE), constrained by some boundary conditions. A computer simulation of such an Initial Boundary Value Problem (IBVP) allows one to predict the state of the system at different moments in time, and the comparison between the model and observations fixes the model parameters. However, both the prediction and the measurement of a real process are prone to multiple types of uncertainties. In this report we present a concept of the inverse uncertainty quantification for a distributed parameter system, useful for identification and quantification of the model uncertainties. First, we build a stochastic model of different types of uncertainties. Next, we perform the sensitivity analysis in order to understand their effects on the model and the measurements. Finally, we apply the Bayesian inference in order to solve the ill-posed inverse problem of extracting the model parameters and their errors. We illustrate the method with the example of parameter calibration for a glass forming model.