  Retrieving the physical parameters from spectroscopic observations of
exoplanets is key to understanding their atmospheric properties. Exoplanetary
atmospheric retrievals are usually based on approximate Bayesian inference and
rely on sampling-based approaches to compute parameter posterior distributions.
Accurate or repeated retrievals, however, can result in very long computation
times due to the sequential nature of sampling-based algorithms. We aim to
amortize exoplanetary atmospheric retrieval using neural posterior estimation
(NPE), a simulation-based inference algorithm based on variational inference
and normalizing flows. In this way, we aim (i) to strongly reduce inference
time, (ii) to scale inference to complex simulation models with many nuisance
parameters or intractable likelihood functions, and (iii) to enable the
statistical validation of the inference results. We evaluate NPE on a radiative
transfer model for exoplanet spectra petitRADTRANS, including the effects of
scattering and clouds. We train a neural autoregressive flow to quickly
estimate posteriors and compare against retrievals computed with MultiNest. NPE
produces accurate posterior approximations while reducing inference time down
to a few seconds. We demonstrate the computational faithfulness of our
posterior approximations using inference diagnostics including posterior
predictive checks and coverage, taking advantage of the quasi-instantaneous
inference time of NPE. Our analysis confirms the reliability of the approximate
posteriors produced by NPE. The accuracy and reliability of the inference
results produced by NPE establishes it as a promising approach for atmospheric
retrievals. Amortization of the posterior inference makes repeated inference on
several observations computationally inexpensive since it does not require
on-the-fly simulations, making the retrieval efficient, scalable, and testable.
