$\texttt{PineTree}$: A generative, fast, and differentiable halo model for wide-field galaxy surveys

Mock halo catalogues are indispensable data products for developing and validating cosmological inference pipelines. A major challenge in generating mock catalogues is modelling the halo or galaxy bias, which is the mapping from matter density to dark matter halos or observable galaxies. To this end, N-body codes produce state-of-the-art catalogues. However, generating large numbers of these N-body simulations for big volumes, requires significant computational time. We introduce and benchmark a differentiable and physics-informed neural network that can generate mock halo catalogues of comparable quality to those obtained from full N-body codes. The model design is computationally efficient for the training procedure and the production of large mock suites. We present a neural network, relying only on 18 to 34 trainable parameters, that produces halo catalogues from dark matter overdensity fields. The reduction of network weights is realised through incorporating symmetries motivated by first principles into our model architecture. We train our model using dark matter only N-body simulations across different resolutions, redshifts, and mass bins. We validate the final mock catalogues by comparing them to N-body halo catalogues using different N-point correlation functions. Our model produces mock halo catalogues consistent with the reference simulations, showing that this novel network is a promising way to generate mock data for upcoming wide-field surveys due to its computational efficiency. Moreover, we find that the network can be trained on approximate overdensity fields to reduce the computational cost further. We also present how the trained network parameters can be interpreted to give insights into the physics of structure formation. Finally, we discuss the current limitations of our model as well as more general requirements and pitfalls for approximate halo mock generation.