Abstract: Dark matter halos are the fundamental building blocks of cosmic large-scale structure. Improving our theoretical understanding of their structure, evolution, and formation is an essential step toward understanding how galaxies form, which in turn will allow us to fully exploit the large amount of data from future large-volume galaxy surveys. Although N-body simulations are the only tool to fully compute the nonlinear gravitational evolution of halos, it is difficult to gain physical interpretation from numerical studies alone. I will present a machine-learning approach that aims to provide new physical insights into the physics driving halo formation. We train a machine-learning algorithm to learn cosmological structure formation directly from N-body simulations. The algorithm infers the relationship between the initial conditions and the final dark matter halos, based on inputs describing different properties of the local environment surrounding the dark matter particles in the initial conditions. By evaluating the predictive performance of the algorithm when provided with different types of information, we are able to infer which aspects of the early-Universe density field impact the formation of the final dark matter halos. In general, our approach can be extended to yield physical understanding of other complex nonlinear processes in the context of cosmological structure formation and beyond.