Realistic On-the-fly Outcomes of Planetary Collisions: Machine Learning Applied to Simulations of Giant Impacts

Abstract

Planet formation simulations are capable of directly integrating the evolution of hundreds to thousands of planetary embryos and planetesimals, as they accrete pairwise to become planets. In principle such investigations allow us to better understand the final configuration and geochemistry of the terrestrial planets, as well as to place our solar system in the context of other exosolar systems. These simulations, however, classically prescribe collisions to result in perfect mergers, but computational advances have begun to allow for more complex outcomes to be implemented. Here we apply machine learning to a large but sparse database of giant impact studies, streamlining simulations into a classifier of collision outcomes and a regressor of accretion efficiency. The classifier maps a 4-Dimensional parameter space (target mass, projectile-to-target mass ratio, impact velocity, impact angle) into the four major collision types: merger, "graze-and-merge", "hit-and-run", and disruption. The definition of the four regimes and their boundary is fully data-driven; the results do not suffer from any model assumption in the fitting. The classifier maps the structure of the parameter space and provides insights about the outcome regimes. The regressor is a neural network which is trained to closely mimic the functional relationship between the 4-D space of collision parameters, and a real-variable outcome, the mass of the largest remnant. This work is a prototype of a more complete surrogate model, based on extended sets of simulations ("big data"), that will quickly and reliably predict specific collision outcomes for use in realistic N -body dynamical studies of planetary formation.

Machine learning applied to simulations of collisions between rotating, differentiated planets

“…Future datasets may provide better convergence, however with the current data they are not suitable for training data-driven models. The remnant angular momenta converge quickly and are therefore better suited for studying rotation proved promising (Cambioni et al 2019). Techniques from UQ have also achieved considerable success in other areas of astrophysics investigating high-dimensional emulation (Knabenhans et al 2019) (hereafter we refer to ML and UQ as "data-driven" techniques).…”

“…Here, y i is the ith expected value,ȳ is the mean of the expected distribution, andŷ i is the ith predicted value. The r 2 -score has been used as the performance metric in similar work (Cambioni et al 2019) and is therefore a prudent choice in order to make comparisons to other studies. In addition to the r 2 -score, which quantifies the regression performance globally, we also consider the residuals as a function of each individual pre-impact property.…”

“…In recent years, the rise of machine learning and access to increasing computing power have enabled new datadriven approaches. Now, with sufficiently large datasets, surrogate models known as emulators can be trained to predict the outcome of collisions "on-the-fly" (i.e., within N-body simulations) (Cambioni et al 2019). These emulators are lightweight enough to be integrated directly into existing N-body codes (Emsenhuber et al 2020) and, once trained, can make near-instantaneous predictions of collision outcomes.…”

“…In this paper, we show that they can far outperform existing analytic and semi-analytic methods. Nascent efforts to emulate collision outcomes have explored artificial neural networks (ANN) (Cambioni et al 2019;Valencia et al 2019). These studies have shown that simple ANNs can achieve high accuracy on relatively small datasets (N = 800).…”

Gravity-dominated Collisions: A Model for the Largest Remnant Masses with Treatment for “Hit and Run” and Density Stratification

“…With a true hybrid method beyond reach, at least in the near term, efforts have focused instead on characterizing the parameter space of giant-impact outcomes and constructing analytical relationships to link the pre-impact parameters to the post-impact outcomes in models that serve as a surrogate for SPH. Fully data-driven methods are also possible such as interpolation or machine learning ( Cambioni et al 2019 ), which do not rely on underlying assumptions of human-derived analytical forms. Ideally, the models apply to a large range of conditions and scales (i.e., total colliding mass).…”