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Title: Accelerating Giant Impact Simulations with Machine Learning
Authors: Caleb Lammers et al.
First Author’s Institution: Princeton University
Status: Published in ApJ
Planet Formation
In the nebular hypothesis view of planet formation, planets form out of a protoplanetary disk, starting out as small dust grains, some of which combine and grow to form planetesimals and eventually planets. Part of this process is the giant-impact phase, in which the planetesimals experience frequent, violent collisions, leading to the growth of what will eventually become fully fledged planets.
Numerically modeling the giant-impact phase is complicated by the computational difficulty of running simulations of many bodies over long timescales. Machine learning has already been adopted to improve and speed up planetary simulations, such as with the Stability of Planetary Orbital Configurations Klassifier (SPOCK) package. SPOCK’s first incarnation (SPOCKI) predicts whether a compact planetary system is stable over 1,000,000,000 orbits based on the results of a shorter 10,000-orbit integration, and an extension (SPOCKII) uses those results to predict when a planetary system will destabilize.
Creating a Machine Learning™ Framework
Today’s article extends previous work by using machine learning to predict the outcomes of planet–planet collisions in three-planet systems with two subtasks: 1) predicting which planet pair will collide and 2) predicting the orbital configuration of the resulting system. The authors use supervised learning: giving a model a training set with inputs and correct outputs so that the model can learn the mapping from inputs to outputs. Predicting collisions (subtask 1) requires classification, producing an outcome from a set of discrete options or categories (in this case, which planets collide). Predicting resulting orbital configurations (subtask 2) requires regression, producing numerical values describing the orbit of the post-collision system. The authors use a training set of more than 500,000 N-body simulations integrated with the REBOUND package. They initialize tightly packed three-planet systems with randomized initial conditions and integrate the systems for 10,000,000 orbits (of the innermost planet) with mass and momentum conservation. The authors only keep the systems with mergers between 10,000 and 10,000,000 orbits so the machine learning framework does not concern itself with non-merging systems.
The authors use separate multi-layer perceptron models independently trained on 80% of the training set (leaving the rest as a validation set) to complete both subtasks, following the schematic shown in Figure 1. The collision classifier takes as inputs the orbital elements of the three planets after they’ve completed 10,000 orbits, generates the probabilities of planet-pair collisions, and samples the probabilities to determine which pair of planets collide. The orbital outcome regressor takes the orbital elements of the three planets and the choice of which planets collide to predict the new orbital elements (semi-major axis, eccentricity, and inclination) of the resulting system.
Figure 1: A schematic of the machine learning model in which a classifier predicts which pair among three planets collides and a regressor predicts the orbital configuration of the two resulting planets. [Lammers et al. 2024]
Piecing Together the Giant-Impact Emulator
The authors combine their machine learning model with SPOCKII to create an iterative emulator to model the giant-impact phase, with a schematic shown in Figure 2. The emulator takes in overly packed, multi-planet systems with randomly initialized configurations, groups the systems into trios of planets, uses SPOCKII to predict when the systems will destabilize, merges the most unstable trio, and then repeats until stability is achieved. The authors also run N-body simulations for 500 ten-planet systems for comparison with the results of the emulator. As shown in Figure 3, there is close agreement with masses, spacings, inclinations, and most system-level properties.
Figure 2: A schematic of the giant-impact emulator in which a multi-planet system is broken into trios. The machine learning model shown in Figure 1 predicts the results of a collision in the most unstable trio, and the process repeats until a stable system is formed. [Lammers et al. 2024]
Figure 3: A comparison of the properties of the N-body (red) and machine learning–based (blue) planetary systems resulting from giant impacts. The machine learning–based framework produces largely similar results except that machine learning tends to produce systems that are less dynamically excited (bottom right). [Lammers et al. 2024]
Planet formation is a messy, unsolved problem. Until the discovery of exoplanetary systems, we had only the solar system and its single formation outcome to study. It turns out that nature produces a beautiful mosaic of planetary systems, many of which bear little resemblance to our own. The giant-impact phase has long been a bottleneck in simulating planet formation due to computational constraints, and today’s article presents a truly exciting advancement in modeling planet–planet collisions. The model is limited in that it breaks multi-planet systems into trios of adjacent planets and models collisions and scattering only within trios, though the authors expect this is a minor effect. The model is publicly available and will certainly expand the frontier of possible planet formation analyses.
Original astrobite edited by Nathalie Korhonen Cuestas.
About the author, Kylee Carden:
I am a second-year PhD student at The Ohio State University, where I am an observer of planets outside the solar system. I’m involved with the Roman Space Telescope, a small robotic telescope called DEMONEXT, and exoplanet atmospheres. I am a huge fan of my cat Piccadilly, cycling, and visiting underappreciated tourist sites.