Accelerating Giant Impact Simulations with Machine Learning

TL;DR

An ML model is developed that can accurately predict which two planets will experience a collision, along with the state of the postcollision planets, from a short integration of the system’s initial conditions, and is expected to enable analyses that would not otherwise be computationally feasible.

Abstract

Constraining planet formation models based on the observed exoplanet population requires generating large samples of synthetic planetary systems, which can be computationally prohibitive. A significant bottleneck is simulating the giant impact phase, during which planetary embryos evolve gravitationally and combine to form planets, which may themselves experience later collisions. To accelerate giant impact simulations, we present a machine learning (ML) approach to predicting collisional outcomes in multiplanet systems. Trained on more than 500,000 $N$-body simulations of three-planet systems, we develop an ML model that can accurately predict which two planets will experience a collision, along with the state of the post-collision planets, from a short integration of the system's initial conditions. Our model greatly improves on non-ML baselines that rely on metrics from dynamics theory, which struggle to accurately predict which pair of planets will experience a collision. By combining with a model for predicting long-term stability, we create an ML-based giant impact emulator, which can predict the outcomes of giant impact simulations with reasonable accuracy and a speedup of up to four orders of magnitude. We expect our model to enable analyses that would not otherwise be computationally feasible. As such, we release our training code, along with an easy-to-use API for our collision outcome model and giant impact emulator.

Figures (7)

• Figure 1: Schematic of our machine learning model. The collision classifier takes the mean and standard deviation of the three planets' orbital elements from a short $N$-body integration as input and predicts which pair of planets will collide (in the form of three collision probabilities). The orbital outcome regressor takes the orbital elements, as well as a choice for which two planets to combine, and predicts the orbital elements of the two resulting post-collision planets.
• Figure 2: Performance of the collision classifier model on $200$ random validation systems. The probabilities of a collision occurring between planets $1$ -- $2$, $2$ -- $3$, and $1$ -- $3$, as predicted by the ML model, are plotted against the true fraction of collisions that occur between the planet pairs, determined by performing $250$ shadow integrations of each system. The model accurately predicts collision probabilities with a scatter of ${\sim}\,10$ % and very little bias about the true fractions ($\sigma$ is the root-mean-squared error and $b$ is the mean of the residuals). For comparison, all baseline models we considered performed poorly (see Appendix \ref{['sec:classifer_baseline']}).
• Figure 3: Comparison between the performance of the orbital outcome regressor (top row) and a non-ML baseline model (bottom row) on the validation set of $103$,$404$ three-planet systems. Predicted orbital elements (i.e., semi-major axis, eccentricity, and inclination) for the new, merged planets are plotted against their true orbital elements. The ML model predicts orbital elements with somewhat less scatter and bias about the true values than the baseline model, approaching the accuracy limits imposed by chaos (see Table \ref{['table:performance_comparison']}).
• Figure 4: Same comparison as Fig. \ref{['fig:regression_comparison1']}, now for the three post-collision orbital elements of the surviving planet that is not involved in the merger. The orbital outcome regressor predicts semi-major axis, eccentricity, and inclination with less scatter and bias than the non-ML baseline model, approaching the limit imposed by chaos (see Table \ref{['table:performance_comparison']}).
• Figure 5: Schematic of the iterative giant impact emulator. At each step, instability times for sub-trios of planets are predicted using SPOCKII Cranmer2021. Then, with the machine learning model presented in this work, we predict the collisional outcome of the planet trio with the shortest instability time, replace the trio with the two new planets, and repeat until SPOCKII identifies the system as long-term stable.