  Current endeavours in exoplanet characterisation rely on atmospheric
retrieval to quantify crucial physical properties of remote exoplanets from
observations. However, the scalability and efficiency of the technique are
under strain with increasing spectroscopic resolution and forward model
complexity. The situation becomes more acute with the recent launch of the
James Webb Space Telescope and other upcoming missions. Recent advances in
Machine Learning provide optimisation-based Variational Inference as an
alternative approach to perform approximate Bayesian Posterior Inference. In
this investigation we combined Normalising Flow-based neural network with our
newly developed differentiable forward model, Diff-Tau, to perform Bayesian
Inference in the context of atmospheric retrieval. Using examples from real and
simulated spectroscopic data, we demonstrated the superiority of our proposed
framework: 1) Training Our neural network only requires a single observation;
2) It produces high-fidelity posterior distributions similar to sampling-based
retrieval and; 3) It requires 75% less forward model computation to converge.
4.) We performed, for the first time, Bayesian model selection on our trained
neural network. Our proposed framework contribute towards the latest
development of a neural-powered atmospheric retrieval. Its flexibility and
speed hold the potential to complement sampling-based approaches in large and
complex data sets in the future.
