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

Abstract

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available but seemingly useless data are ignored. This work proposes incorporating such data from additional physical fields into the inverse analysis, even when the forward model solves a single-physics problem. A Bayesian framework easily incorporates the additional data and quantifies the resulting uncertainty reduction. We formally introduce the proposed method, which we denote as multi-physics-enhanced Bayesian inverse analysis. Moreover, this work is the first to quantify the reduction in parameter uncertainty by comparing the information gain from the prior to the posterior when using single-physics versus multi-physics data. We demonstrate the potential of the proposed method in two exemplary applications. Our results show that even a few or noisy data points from an additional physical field can considerably increase the information gain, even when the physical field is only weakly or one-way coupled. Overall, 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, particularly in medicine.