  Characterizing exoplanetary atmospheres via Bayesian retrievals requires
assuming some chemistry model, such as thermochemical equilibrium or
parameterized abundances. The higher-resolution data offered by upcoming
telescopes enables more complex chemistry models within retrieval frameworks.
Yet, many chemistry codes that model more complex processes like photochemistry
and vertical transport are computationally expensive, and directly
incorporating them into a 1D retrieval model can result in prohibitively long
execution times. Additionally, phase-curve observations with upcoming
telescopes motivate 2D and 3D retrieval models, further exacerbating the
lengthy runtime for retrieval frameworks with complex chemistry models. Here,
we compare thermochemical equilibrium approximation methods based on their
speed and accuracy with respect to a Gibbs energy-minimization code. We find
that, while all methods offer orders of magnitude reductions in computational
cost, neural network surrogate models perform more accurately than the other
approaches considered, achieving a median absolute dex error <0.03 for the
phase space considered. While our results are based on a 1D chemistry model,
our study suggests that higher dimensional chemistry models could be
incorporated into retrieval models via this surrogate modeling approach.
