@article{jha2022goal,
title = {Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation},
journal = {Journal of Computational Physics},
volume = {470},
pages = {111575},
year = {2022},
issn = {0021-9991},
doi = {10.1016/j.jcp.2022.111575},
url = {https://www.sciencedirect.com/science/article/pii/S0021999122006374},
author = {Prashant K. Jha and J. Tinsley Oden},
keywords = {Bayesian inference, A-posterior estimates, Model calibration, Variational formulation, Uncertainty quantification, Goal-oriented a-posterior estimates},
abstract = {In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.}
}