Multi-Physics-Enhanced Bayesian Inverse Analysis: Information Gain from Additional Fields

Abstract: Many real-world inverse problems suffer from limited data, often because they rely on measurements of a single physical field. Such data frequently fail to sufficiently reduce parameter uncertainty in Bayesian inverse analysis. Incorporating easily available data from additional physical fields can substantially decrease this uncertainty. We focus on Bayesian inverse analyses based on computational models, e.g., those using the finite element method. To incorporate data from additional physical fields, the computational model must be extended to include these fields. While this model extension may have little to no effect on forward model predictions, it can greatly enhance inverse analysis by leveraging the multi-physics data. Our work proposes this multi-physics-enhanced inverse approach and demonstrates its potential using two models: a simple model with one-way coupled fields and a complex computational model with fully coupled fields. We quantify the uncertainty reduction by comparing the effect of single-physics and multi-physics data on the information gain from the prior to the posterior. Our results show that even a few or noisy data points from an additional physical field can considerably increase the information gain, even if this field is weakly or one-way coupled. Although multi-physics data are often readily available, it is remarkable that their potential has been largely neglected in model calibration so far. Instead, costly and time-consuming additional experimental setups are often pursued. In contrast, incorporating multi-physics data requires minimal effort when multi-physics models are readily available or easy to implement, as is the case with uncoupled and one-way coupled models. This work proposes and promotes the future use of multi-physics-enhanced Bayesian inverse analysis as a cost- and time-saving game-changer across various fields of science and industry.