🤖 AI Summary
This work proposes a unified Bayesian calibration framework to address the lack of reliable and consistent calibration methods for computationally expensive and data-scarce scenarios. The framework uniquely supports both single-output and multi-output complex models within a coherent formulation and is accompanied by ACBICI, a modular open-source Python library. By integrating uncertainty quantification with Bayesian inference, the approach balances usability and extensibility, establishing a closed loop among theory, implementation, and practical application. The study delivers standardized calibration guidelines tailored to real-world engineering challenges and enhances reproducibility and deployment through its open-source toolkit, significantly improving the reliability and accessibility of calibrating complex scientific and engineering models.
📝 Abstract
In this work, we review the theory involved in the Bayesian calibration of complex computer models, with particular emphasis on their use for applications involving computationally expensive simulations and scarce experimental data. In the article, we present a unified framework that incorporates various Bayesian calibration methods, including well-established approaches. Furthermore, we describe their implementation and use with a new, open-source Python library, ACBICI (A Configurable BayesIan Calibration and Inference Package). All algorithms are implemented with an object-oriented structure designed to be both easy to use and readily extensible. In particular, single-output and multiple-output calibration are addressed in a consistent manner. The article completes the theory and its implementation with practical recommendations for calibrating the problems of interest. These guidelines -- currently unavailable in a unified form elsewhere -- together with the open-source Python library, are intended to support the reliable calibration of computational codes and models commonly used in engineering and related fields. Overall, this work aims to serve both as a comprehensive review of the statistical foundations and (computational) tools required to perform such calculations, and as a practical guide to Bayesian calibration with modern software tools.