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In this article, we present three algorithms for aerosol parameters retrieval from TROPOspheric Monitoring Instrument measurements in the <inline-formula><tex-math notation="LaTeX">$\text {O}_{2}$</tex-math></inline-formula> A-band. These algorithms use neural networks 1) to emulate the radiative transfer model and a Bayesian approach to solve the inverse problem, 2) to learn the inverse model from the synthetic radiances, and 3) to learn the inverse model from the principal-component transform of synthetic radiances. The training process is based on full-physics radiative transfer simulations. The accuracy and efficiency of the neural network based retrieval algorithms are analyzed with synthetic and real data.