Philip M Winter, Christoph Burger, Sebastian Lehner, Johannes Kofler, Thomas I Maindl, and Christoph M Schäfer
Fast and accurate treatment of collisions in the context of modern N-body planet formation simulations remains a challenging task due to inherently complex collision processes. We aim to tackle this problem with machine learning (ML), in particular via residual neural networks. Our model is motivated by the underlying physical processes of the data-generating process and allows for flexible prediction of post-collision states. We demonstrate that our model outperforms commonly used collision handling methods such as perfect inelastic merging and feed-forward neural networks in both prediction accuracy and out-of-distribution generalization. Our model outperforms the current state of the art in 20/24 experiments. We provide a data set that consists of 10164 Smooth Particle Hydrodynamics (SPH) simulations of pairwise planetary collisions. The data set is specifically suited for ML research to improve computational aspects for collision treatment and for studying planetary collisions in general. We formulate the ML task as a multi-task regression problem, allowing simple, yet efficient training of ML models for collision treatment in an end-to-end manner. Our models can be easily integrated into existing N-body frameworks and can be used within our chosen parameter space of initial conditions, i.e. where similar-sized collisions during late-stage terrestrial planet formation typically occur.
Monthly Notices of the Royal Astronomical Society, 520, 1, 1224-1242, 2022-10-14.