  Approximate Bayesian computation (ABC) provides us with a way to infer
parameters of models, for which the likelihood function is not available, from
an observation. Using ABC, which depends on many simulations from the
considered model, we develop an inferential framework to learn parameters of a
stochastic numerical simulator of volcanic eruption. Moreover, the model itself
is parallelized using Message Passing Interface (MPI). Thus, we develop a
nested-parallelized MPI communicator to handle the expensive numerical model
with ABC algorithms. ABC usually relies on summary statistics of the data in
order to measure the discrepancy model output and observation. However,
informative summary statistics cannot be found for the considered model. We
therefore develop a technique to learn a distance between model outputs based
on deep metric-learning. We use this framework to learn the plume
characteristics (eg. initial plume velocity) of the volcanic eruption from the
tephra deposits collected by field-work associated with the 2450 BP Pululagua
(Ecuador) volcanic eruption.
