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Flagship near-future surveys targeting $10^8-10^9$ galaxies across cosmictime will soon reveal the processes of galaxy assembly in unprecedentedresolution. This creates an immediate computational challenge on effectiveanalyses of the full data-set. With simulation-based inference (SBI), it ispossible to attain complex posterior distributions with the accuracy oftraditional methods but with a $>10^4$ increase in speed. However, it comeswith a major limitation. Standard SBI requires the simulated data to haveidentical characteristics to the observed data, which is often violated inastronomical surveys due to inhomogeneous coverage and/or fluctuating sky andtelescope conditions. In this work, we present a complete SBI-basedmethodology, ``SBI$^{++}$,'' for treating out-of-distribution measurementerrors and missing data. We show that out-of-distribution errors can beapproximated by using standard SBI evaluations and that missing data can bemarginalized over using SBI evaluations over nearby data realizations in thetraining set. In addition to the validation set, we apply SBI$^{++}$ togalaxies identified in extragalactic images acquired by the James Webb SpaceTelescope, and show that SBI$^{++}$ can infer photometric redshifts at least asaccurately as traditional sampling methods and crucially, better than theoriginal SBI algorithm using training data with a wide range of observationalerrors. SBI$^{++}$ retains the fast inference speed of $\sim$1 sec for objectsin the observational training set distribution, and additionally permitsparameter inference outside of the trained noise and data at $\sim$1 min perobject. This expanded regime has broad implications for future applications toastronomical surveys.

SBI++: Flexible, Ultra-fast Likelihood-free Inference Customized for Astronomical Applications