This week I presented a new research project at the 2021 AIAA SciTech Forum. You can find a copy of my presentation slides here. Below is a brief summary of the work, for more details check out the recent preprint of our research paper.

A Mathematical and Computational Foundation for Predictive Digital Twins

Current state-of-the-art digital twins are largely the result of custom implementations that require considerable deployment resources and a high level of expertise. We have proposed a unifying mathematical foundation for digital twins, with the goal of moving from the one-off digital twin to accessible and robust digital twin implementations at scale. Specifically, we define the combined asset-twin system in terms of six key quantities, which are shown in the figure below.

The quantities comprising our mathematical abstraction of the asset-twin system

Defining the system in this way enables us to model the evolution of the physical asset and its digital twin over time. The digital twin learns about the state of the physical asset by assimilating incoming observational data. This information is used to update the internal digital twin models, which are then evaluated to provide accurate analysis and predictions. This enables the digital twin to positively influence the physical asset by informing and/or issuing intelligent control inputs. We model this two-way coupled system using the probabilistic graphical model below, which illustrates the dependencies between quantities in the system as it evolves over time.

The Probabilistic Graphical Model we propose to model the dynamical evolution of the asset-twin system

Graphical models are a powerful tool for probabilistic representation, inference, and learning, and have been successfully applied in applications ranging from robotics and computer vision, to speech recognition and medical diagnosis. Our proposed probabilistic graphical model serves as a foundation for defining and modeling a digital twin, as well as deriving computationally efficient algorithms for model updating, prediction, and optimal control. More information about the proposed probabilistic graphical model formulation, as well as a demonstration of how we have used the model to perform principled and scalable experimental calibration of a UAV digital twin, can be found in our research paper.