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An ambitious goal in cosmology is to forward-model the observed distributionof galaxies in the nearby Universe today from the initial conditions oflarge-scale structures. For practical reasons, the spatial resolution at whichthis can be done is necessarily limited. Consequently, one needs a mappingbetween the density of dark matter averaged over ~Mpc scales, and thedistribution of dark matter halos (used as a proxy for galaxies) in the sameregion. Here we demonstrate a method for determining the halo mass distributionfunction by learning the tracer bias between density fields and halo cataloguesusing a neural bias model. The method is based on the Bayesian analysis ofsimple, physically motivated, neural network-like architectures, which wedenote as neural physical engines, and neural density estimation. As a result,we are able to sample the initial phases of the dark matter density fieldwhilst inferring the parameters describing the halo mass distribution function,providing a fully Bayesian interpretation of both the initial dark matterdensity distribution and the neural bias model. We successfully run an upgradedBORG inference using our new likelihood and neural bias model with halocatalogues derived from full N-body simulations. We notice orders of magnitudeimprovement in modelling compared to classical biasing techniques.

Neural physical engines for inferring the halo mass distribution function