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Modern machine learning will allow for simulation-based inference from reionization-era 21cm observations at the Square Kilometre Array. Our framework combines a convolutional summary network and a conditional invertible network through a physics-inspired latent representation. It allows for an efficient and extremely fast determination of the posteriors of astrophysical and cosmological parameters, jointly with well-calibrated and on average unbiased summaries. The sensitivity to non-Gaussian information makes our method a promising alternative to the established power spectra.

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