  A unifying mathematical formulation is needed to move from one-off digital
twins built through custom implementations to robust digital twin
implementations at scale. This work proposes a probabilistic graphical model as
a formal mathematical representation of a digital twin and its associated
physical asset. We create an abstraction of the asset-twin system as a set of
coupled dynamical systems, evolving over time through their respective
state-spaces and interacting via observed data and control inputs. The formal
definition of this coupled system as a probabilistic graphical model enables us
to draw upon well-established theory and methods from Bayesian statistics,
dynamical systems, and control theory. The declarative and general nature of
the proposed digital twin model make it rigorous yet flexible, enabling its
application at scale in a diverse range of application areas. We demonstrate
how the model is instantiated to enable a structural digital twin of an
unmanned aerial vehicle (UAV). The digital twin is calibrated using
experimental data from a physical UAV asset. Its use in dynamic decision making
is then illustrated in a synthetic example where the UAV undergoes an in-flight
damage event and the digital twin is dynamically updated using sensor data. The
graphical model foundation ensures that the digital twin calibration and
updating process is principled, unified, and able to scale to an entire fleet
of digital twins.
