  Atmospheric retrieval determines the properties of an atmosphere based on its
measured spectrum. The low signal-to-noise ratio of exoplanet observations
require a Bayesian approach to determine posterior probability distributions of
each model parameter, given observed spectra. This inference is computationally
expensive, as it requires many executions of a costly radiative transfer (RT)
simulation for each set of sampled model parameters. Machine learning (ML) has
recently been shown to provide a significant reduction in runtime for
retrievals, mainly by training inverse ML models that predict parameter
distributions, given observed spectra, albeit with reduced posterior accuracy.
Here we present a novel approach to retrieval by training a forward ML
surrogate model that predicts spectra given model parameters, providing a fast
approximate RT simulation that can be used in a conventional Bayesian retrieval
framework without significant loss of accuracy. We demonstrate our method on
the emission spectrum of HD 189733 b and find good agreement with a traditional
retrieval from the Bayesian Atmospheric Radiative Transfer (BART) code
(Bhattacharyya coefficients of 0.9843--0.9972, with a mean of 0.9925, between
1D marginalized posteriors). This accuracy comes while still offering
significant speed enhancements over traditional RT, albeit not as much as ML
methods with lower posterior accuracy. Our method is ~9x faster per parallel
chain than BART when run on an AMD EPYC 7402P central processing unit (CPU).
Neural-network computation using an NVIDIA Titan Xp graphics processing unit is
90--180x faster per chain than BART on that CPU.
