  Interpreting the observations of exoplanet atmospheres to constrain physical
and chemical properties is typically done using Bayesian retrieval techniques.
Because these methods require many model computations, a compromise is made
between model complexity and run time. Reaching this compromise leads to the
simplification of many physical and chemical processes (e.g. parameterised
temperature structure). Here we implement and test sequential neural posterior
estimation (SNPE), a machine learning inference algorithm, for exoplanet
atmospheric retrievals. The goal is to speed up retrievals so they can be run
with more computationally expensive atmospheric models, such as those computing
the temperature structure using radiative transfer. We generate 100 synthetic
observations using ARCiS (ARtful Modeling Code for exoplanet Science, an
atmospheric modelling code with the flexibility to compute models in varying
degrees of complexity) and perform retrievals on them to test the faithfulness
of the SNPE posteriors. The faithfulness quantifies whether the posteriors
contain the ground truth as often as we expect. We also generate a synthetic
observation of a cool brown dwarf using the self-consistent capabilities of
ARCiS and run a retrieval with self-consistent models to showcase the
possibilities that SNPE opens. We find that SNPE provides faithful posteriors
and is therefore a reliable tool for exoplanet atmospheric retrievals. We are
able to run a self-consistent retrieval of a synthetic brown dwarf spectrum
using only 50,000 forward model evaluations. We find that SNPE can speed up
retrievals between $\sim2\times$ and $\geq10\times$ depending on the
computational load of the forward model, the dimensionality of the observation,
and the signal-to-noise ratio of the observation. We make the code publicly
available for the community on Github.
