We explore an amortised implicit inference approach to estimate from optical absorption spectra the posterior distributions of metallicities and star formation histories (SFHs) of galaxies, i.e. star formation rate as a function of time. We generate a sample of synthetic spectra to train and test our model in a simulation-based inference workflow using the spectroscopic predictions of the MILES stellar population library and non-parametric SFHs.

We reliably estimate the mass assembly of an integrated stellar population with well-calibrated uncertainties. We then apply the pipeline to real observations of massive elliptical galaxies, recovering the well-known relationship between age and velocity dispersion, and show that the most massive galaxies build up to 90% of their total stellar masses 1 Gyr after the Big Bang. The measurements also agree with state-of-the-art inversion codes, but the inference is performed up to five orders of magnitude faster.

This machine learning-based implicit inference applied to full spectral fitting makes it possible to address large numbers of galaxies while performing a thick sampling of the posteriors. It allows to estimate both the deterministic trends and the inherent uncertainties of the highly degenerate inversion problem, so far inaccessible, dealing with the size and complexity of upcoming spectroscopic surveys such as DESI, WEAVE or 4MOST.