Accelerating Giant Impact Simulations with Machine Learning (2408.08873v2)

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 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.

• The paper demonstrates an ML model that predicts planetary collisions and post-collision orbits with an RMSE of approximately 10%.
• It integrates a collision classifier and orbital outcome regressor to significantly reduce simulation times compared to traditional N-body methods.
• The emulator achieves up to a 10,000x speedup, enabling broader exploration of parameter spaces in planetary formation research.

Accelerating Giant Impact Simulations with Machine Learning

The paper, "Accelerating Giant Impact Simulations with Machine Learning," by Caleb Lammers and colleagues presents a ML framework designed to hasten the process of simulating giant impacts in multiplanet systems. Traditional $N$-body simulations for modeling these collisions are computationally intensive, limiting the scope of studies in planetary formation. This work addresses this challenge by developing and validating an ML-based approach that significantly reduces computational overhead while maintaining high accuracy.

Core Contributions

The primary contributions of this paper are twofold: an ML model capable of predicting which planets will collide and the orbital characteristics of the resultant post-collision planets, as well as an ML-based giant impact emulator. The emulator integrates the ML model with prior work using the SPOCKII framework for predicting system stability, resulting in a holistic tool for planet formation simulations.

Methodology

The authors trained their model on over 500,000 $N$-body simulations of three-planet systems, producing a robust dataset for ML application. The model consists of two parts:

1. Collision Classifier: This classifier predicts which pair of planets will collide by analyzing the mean and standard deviation of the planets' orbital elements from a short $10^4$ orbit integration.
2. Orbital Outcome Regressor: This regressor predicts the orbital elements of the post-collision planets.

Significantly, these models, based on multilayer perceptrons (MLPs), outperform non-ML baselines that rely on dynamics-theory metrics, showcasing improved accuracy in predicting collision probabilities and post-collision orbital configurations.

Numerical Results and Performance Evaluation

For collision prediction, the ML model demonstrates a root-mean-squared error (RMSE) of approximately 10%, substantially better than any tested non-ML model. Regarding the orbital outcome prediction, the ML model achieves prediction accuracies that approach the limits imposed by the chaotic nature of multiplanet systems. This includes near-exact conservation of angular momentum and energy during the simulations.

Implications and Future Directions

The implications of this research are notable for both practical and theoretical planetary science. Practically, the ML-based emulator presents a speedup of up to four orders of magnitude over traditional $N$-body simulations. This acceleration permits the exploration of larger parameter spaces and the simulation of a broader range of initial conditions, previously computationally intractable.

The research also opens several avenues for future work. Improving the integration with stability prediction models like SPOCKII could further refine the precision and efficiency of the simulations. Additionally, extending the ML model to handle more complex multi-planet interactions beyond three-planet systems could enrich the scope of its applicability.

In conclusion, this paper makes substantial strides in enhancing the feasibility and scope of simulating planetary formation via giant impacts. The ML-based methodology proves to be a significant advancement over traditional approaches, providing a vital tool for ongoing and future investigations in planetary dynamics and formation models. By enabling rapid, large-scale simulations, it stands to significantly impact our understanding of planetary system evolution.