A digital twin is a computer model that represents an individual, for example, a component, a patient or a process. In many situations, we want to gain knowledge about an individual from its data while incorporating imperfect physical knowledge and also learn from data from other individuals. In this paper, we introduce a fully Bayesian methodology for learning between digital twins in a setting where the physical parameters of each individual are of interest. A model discrepancy term is incorporated in the model formulation of each personalized model to account for the missing physics of the low-fidelity model. To allow sharing of information between individuals, we introduce a Bayesian Hierarchical modelling framework where the individual models are connected through a new level in the hierarchy. Our methodology is demonstrated in two case studies, a toy example previously used in the literature extended to more individuals and a cardiovascular model relevant for the treatment of Hypertension. The case studies show that 1) models not accounting for imperfect physical models are biased and over-confident, 2) the models accounting for imperfect physical models are more uncertain but cover the truth, 3) the models learning between digital twins have less uncertainty than the corresponding independent individual models, but are not over-confident.

翻译：数字孪生是一种代表个体（例如组件、患者或过程）的计算机模型。在许多情况下，我们希望从个体数据中获取知识，同时整合不完善的物理知识，并学习其他个体的数据。本文针对每个个体物理参数均具有研究价值的场景，提出了一种用于数字孪生间学习的全贝叶斯方法。在每个个性化模型的模型公式中，引入模型差异项以解释低保真模型缺失的物理机制。为实现个体间的信息共享，我们构建了贝叶斯分层建模框架，通过层级中的新层连接各个体模型。通过两个案例研究验证了该方法：一个是文献中曾使用的扩展至更多个体的玩具示例，另一个是与高血压治疗相关的心血管模型。案例研究表明：1）未考虑不完善物理模型的模型存在偏差且过度自信；2）考虑不完善物理模型的模型不确定性更高但覆盖了真实值；3）数字孪生间学习模型的不确定性低于相应的独立个体模型，且不会过度自信。