Embedding model form uncertainties for Bayesian inference of discrepant simulations
- Simulation models are widely used to generate valuable insights into complex physical systems. To accurately reflect system behavior, these models require updates to their governing parameters based on system measurements. Bayesian inference methodologies are particularly attractive for this purpose, as they quantify parameter uncertainty. However, simulation models inherently exhibit discrepancies with observed measurements, as they cannot perfectly replicate the infinitely complex reality. Ignoring these discrepancies leads to overconfident estimations of the inferred posterior distributions, potentially centering around incorrect parameters. This issue affects the calculation of predictions and Quantities of Interest (QoIs), resulting in overly concentrated posterior distributions. The most common framework for incorporating model form uncertainty was developed by Kennedy and O’Hagan, which introduces a flexible discrepancy term that is inferred alongside model parameters. However,Simulation models are widely used to generate valuable insights into complex physical systems. To accurately reflect system behavior, these models require updates to their governing parameters based on system measurements. Bayesian inference methodologies are particularly attractive for this purpose, as they quantify parameter uncertainty. However, simulation models inherently exhibit discrepancies with observed measurements, as they cannot perfectly replicate the infinitely complex reality. Ignoring these discrepancies leads to overconfident estimations of the inferred posterior distributions, potentially centering around incorrect parameters. This issue affects the calculation of predictions and Quantities of Interest (QoIs), resulting in overly concentrated posterior distributions. The most common framework for incorporating model form uncertainty was developed by Kennedy and O’Hagan, which introduces a flexible discrepancy term that is inferred alongside model parameters. However, this approach does not preserve the physicality of the predictions nor facilitate the propagation of model form uncertainty to other QoIs. To address these limitations, Sargsyan proposed embedding the discrepancy term in the parameter formulation as a stochastic extension. This work demonstrates our own explainable framework for embedding model form uncertainties in the Bayesian system of complex engineering systems. Our framework emphasizes the interpretability of discrepancy terms, quantifies uncertainties for models with significant discrepancies relative to measurements and high noise levels, and fully propagates these uncertainties to QoIs for reliable statistical analysis. We apply this framework to a thermal compensation model for the structural health monitoring system of a bridge, illustrating its potential for enhancing decision-making in engineering applications.…

