  The substantial computational cost of high-fidelity models in numerical
hemodynamics has, so far, relegated their use mainly to offline treatment
planning. New breakthroughs in data-driven architectures and optimization
techniques for fast surrogate modeling provide an exciting opportunity to
overcome these limitations, enabling the use of such technology for
time-critical decisions. We discuss an application to the repair of multiple
stenosis in peripheral pulmonary artery disease through either transcatheter
pulmonary artery rehabilitation or surgery, where it is of interest to achieve
desired pressures and flows at specific locations in the pulmonary artery tree,
while minimizing the risk for the patient. Since different degrees of success
can be achieved in practice during treatment, we formulate the problem in
probability, and solve it through a sample-based approach. We propose a new
offline-online pipeline for probabilsitic real-time treatment planning which
combines offline assimilation of boundary conditions, model reduction, and
training dataset generation with online estimation of marginal probabilities,
possibly conditioned on the degree of augmentation observed in already repaired
lesions. Moreover, we propose a new approach for the parametrization of
arbitrarily shaped vascular repairs through iterative corrections of a
zero-dimensional approximant. We demonstrate this pipeline for a diseased model
of the pulmonary artery tree available through the Vascular Model Repository.
