We train a machine learning algorithm to learn cosmological structure formation from N-body simulations. The algorithm infers the relationship between the initial conditions and the final dark matter haloes, without the need to introduce approximate halo collapse models. We gain insights into the physics driving halo formation by evaluating the predictive performance of the algorithm when provided with different types of information about the local environment around dark matter particles. The algorithm learns to predict whether or not dark matter particles will end up in haloes of a given mass range, based on spherical overdensities. We show that the resulting predictions match those of spherical collapse approximations such as extended Press-Schechter theory. Additional information on the shape of the local gravitational potential is not able to improve halo collapse predictions; the linear density field contains sufficient information for the algorithm to also reproduce ellipsoidal collapse predictions based on the Sheth-Tormen model. We investigate the algorithm's performance in terms of halo mass and radial position and perform blind analyses on independent initial conditions realisations to demonstrate the generality of our results.

We present a generalization of our recently proposed machine learning framework, aiming to provide new physical insights into dark matter halo formation. We investigate the impact of the initial density and tidal shear fields on the formation of haloes over the mass range 11.4 ≤ log(M/M ) ≤ 13.4. The algorithm is trained on an N-body simulation to infer the final mass of the halo to which each dark matter particle will later belong. We then quantify the difference in the predictive accuracy between machine learning models using a metric based on the Kullback-Leibler divergence. We first train the algorithm with information about the density contrast in the particles' local environment. The addition of tidal shear information does not yield an improved halo collapse model over one based on density information alone; the difference in their predictive performance is consistent with the statistical uncertainty of the density-only based model. This implies that our machine learning setup does not identify any significant role for the tidal shear in determining halo masses. This result is confirmed as we verify the ability of the initial conditions-to-halo mass mapping learnt from one simulation to generalize to independent simulations. Our work illustrates the broader potential of developing interpretable machine learning frameworks to gain physical understanding of non-linear large-scale structure formation.

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Understanding the impact of environment on the formation and evolution of dark matter halos and galaxies is a crucial open problem. Studying statistical correlations in large simulated populations sheds some light on these impacts, but the causal effect of an environment on individual objects is harder to pinpoint. Addressing this, we present a new method for resimulating a single dark matter halo in multiple large-scale environments. In the initial conditions, we ‘splice’ (i.e. insert) the Lagrangian region of a halo into different Gaussian random fields, while enforcing consistency with the statistical properties of ΛCDM. Applying this technique, we demonstrate that the mass of halos is primarily determined by the density structure inside their Lagrangian patches, while the halos’ concentration is more strongly affected by environment. The splicing approach will also allow us to study, for example, the impact of the cosmic web on accretion processes and galaxy quenching.