  The identification of the Purkinje conduction system in the heart is a
challenging task, yet essential for a correct definition of cardiac digital
twins for precision cardiology. Here, we propose a probabilistic approach for
identifying the Purkinje network from non-invasive clinical data such as the
standard electrocardiogram (ECG). We use cardiac imaging to build an
anatomically accurate model of the ventricles; we algorithmically generate a
rule-based Purkinje network tailored to the anatomy; we simulate physiological
electrocardiograms with a fast model; we identify the geometrical and
electrical parameters of the Purkinje-ECG model with Bayesian optimization and
approximate Bayesian computation. The proposed approach is inherently
probabilistic and generates a population of plausible Purkinje networks, all
fitting the ECG within a given tolerance. In this way, we can estimate the
uncertainty of the parameters, thus providing reliable predictions. We test our
methodology in physiological and pathological scenarios, showing that we are
able to accurately recover the ECG with our model. We propagate the uncertainty
in the Purkinje network parameters in a simulation of conduction system pacing
therapy. Our methodology is a step forward in creation of digital twins from
non-invasive data in precision medicine. An open source implementation can be
found at http://github.com/fsahli/purkinje-learning
