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 Bhattacharyya coefficients of 97.74 – 99.74 % between our 1D marginalized posterior distributions and those of the Bayesian Atmospheric Radiative Transfer ( BART ) code . Our retrieval method is { \sim } 20 \times faster than BART when run on an Intel i7-4770 central processing unit ( CPU ) . Neural-network computation using an NVIDIA Titan Xp graphics processing unit is { \sim } 600 \times faster than BART on that CPU .