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

Abstract

In the late stages of terrestrial planet formation, pairwise collisions between planetary-sized bodies act as the fundamental agent of planet growth. These collisions can lead to either growth or disruption of the bodies involved and are largely responsible for shaping the final characteristics of the planets. Despite their critical role in planet formation, an accurate treatment of collisions has yet to be realized. While semi-analytic methods have been proposed, they remain limited to a narrow set of post-impact properties and have only achieved relatively low accuracies. However, the rise of machine learning and access to increased computing power have enabled novel data-driven approaches. In this work, we show that data-driven emulation techniques are capable of classifying and predicting the outcome of collisions with high accuracy and are generalizable to any quantifiable post-impact quantity. In particular, we focus on the dataset requirements, training pipeline, and classification and regression performance for four distinct data-driven techniques from machine learning (ensemble methods and neural networks) and uncertainty quantification (Gaussian processes and polynomial chaos expansion). We compare these methods to existing analytic and semi-analytic methods. Such data-driven emulators are poised to replace the methods currently used in N-body simulations, while avoiding the cost of direct simulation. This work is based on a new set of 14,856 SPH simulations of pairwise collisions between rotating, differentiated bodies at all possible mutual orientations.

GENGA. II. GPU Planetary N-body Simulations with Non-Newtonian Forces and High Number of Particles

“…When an external code is used to resolve collisions in more detail (e.g., Timpe et al 2020), it is necessary to stop the entire simulation at the time of the first detected collision, or at the earliest back-traced collision time. It is important that all other particles, which are not involved in the collision or in a close encounter, are also integrated backward in time self consistently.…”

Collision Chains among the Terrestrial Planets. III. Formation of the Moon

“…Even when giant impacts are properly and accurately computed by a code, they are sensitive to relatively minor changes in impact angle, velocity, composition, and mass ratio (roughly in that order; see Timpe et al 2020). Strong variation is observed within common ranges of those parameters (Gabriel et al 2020).…”

“…where γ = m imp /m tar is the mass ratio and sin(θ coll ) is equivalent to the normalized impact parameter b/(r imp + r tar ). Composition, as represented by a variable core mass fraction Z, introduces another dimensionless parameter that affects collisions systematically (Timpe et al 2020).…”

“…The training data (Reufer 2011;Gabriel et al 2020) are high-resolution simulations, about 200,000 SPH particles total, of gi-ant impacts starting from nonrotating bodies of 30/70 wt% iron/forsterite composition. A more expansive parameter sampling was generated by Timpe et al (2020), although at lower resolution (10,000 particles in the projectile). This enabled a more general assessment of machine-learning approaches, applied to a dataset that includes preimpact rotation and compositional variation.…”

Collision Chains among the Terrestrial Planets. II. An Asymmetry between Earth and Venus

“…First, the most common orientation is for impact orientation and spin to be perpendicular, which provide little angular moment. The second reason is that pre-impact spin affects the outcomes less than the other effects we study here (Timpe et al 2020). We provide several new outputs of the simulations compared to Paper I that are related to the SPH modeling of possible return collisions.…”