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Fast and automated inference of binary-lens, single-source (2L1S)microlensing events with sampling-based Bayesian algorithms (e.g., Markov ChainMonte Carlo; MCMC) is challenged on two fronts: high computational cost oflikelihood evaluations with microlensing simulation codes, and a pathologicalparameter space where the negative-log-likelihood surface can contain amultitude of local minima that are narrow and deep. Analysis of 2L1S eventsusually involves grid searches over some parameters to locate approximatesolutions as a prerequisite to posterior sampling, an expensive process thatoften requires human-in-the-loop domain expertise. As the next-generation,space-based microlensing survey with the Roman Space Telescope is expected toyield thousands of binary microlensing events, a new fast and automated methodis desirable. Here, we present a likelihood-free inference (LFI) approach namedamortized neural posterior estimation, where a neural density estimator (NDE)learns a surrogate posterior $\hat{p}(\theta|x)$ as an observation-parametrizedconditional probability distribution, from pre-computed simulations over thefull prior space. Trained on 291,012 simulated Roman-like 2L1S simulations, theNDE produces accurate and precise posteriors within seconds for any observationwithin the prior support without requiring a domain expert in the loop, thusallowing for real-time and automated inference. We show that the NDE alsocaptures expected posterior degeneracies. The NDE posterior could then berefined into the exact posterior with a downstream MCMC sampler with minimalburn-in steps.

Real-Time Likelihood-Free Inference of Roman Binary Microlensing Events with Amortized Neural Posterior Estimation