  We present a probabilistic deep learning methodology that enables the
construction of predictive data-driven surrogates for stochastic systems.
Leveraging recent advances in variational inference with implicit
distributions, we put forth a statistical inference framework that enables the
end-to-end training of surrogate models on paired input-output observations
that may be stochastic in nature, originate from different information sources
of variable fidelity, or be corrupted by complex noise processes. The resulting
surrogates can accommodate high-dimensional inputs and outputs and are able to
return predictions with quantified uncertainty. The effectiveness our approach
is demonstrated through a series of canonical studies, including the regression
of noisy data, multi-fidelity modeling of stochastic processes, and uncertainty
propagation in high-dimensional dynamical systems.
