A new approach to forecast stability maps around planetary system
Authors: Pinheiro Tiago , Sfair Rafael , Ramon Giovana 
Published: July 2024

Stability maps of planetary system can be carry out through numerical simulations, which require lot of computational efforts. This project propose a machine learning approach to forecast stable orbits around a planet. We generated our dataset used to train and test machine learning algorithms by runing an ensemble of 100,000 dimensionless numerical simulations of the three-body problem. In these simulations, we modeled a system with a star, a planet, and a test particle in an S-type orbit around the planet using. Rebound package and IAS15 integrator. The dataset is composed of nine features that represent the initial conditions of each numerical simulation. These features include the mass ratio of the system, planet eccentricity and true anomaly, particle orbital elements such as semi-major axis, eccentricity, inclination, argument of pericenter, longitude of node, and true anomaly. Each data point in our dataset is labeled as either stable or unstable. Everytime when the particle collided with massive bodies or was ejected from the system was consider unstable, if the particle survived throughout the entire simulation, it was classified as stable.The overall outcome of our numerical simulations shows that 11.83% of samples in the dataset represent stable systems, while 88.17% are unstable. Among the unstable samples, 47.22% particles collided with the planet, and 40.95% were ejected from the system. This imbalance in class distribution can introduce biases and diminish the effectiveness of algorithm performance. To tackle with this issue, we evaluated the performance of our machine learning model using five different resampling techniques: random undersampling, random oversampling, SMOTE, Borderline SMOTE, and ADASYN. We also explored the option without using any resample methods.In this project, we employed 5 machine learning algorithms: Decision Tree, and ensemples of Decision Tree, such as Random Forest, XGboost (Extreme Gradient Boosting), LightGBM (Light Gradient-Boosting Machine), Histogram Gradient Boosting. Searching for best machine learning model, we conducted hyperparameter and threshold tuning. Hyperparameters are the parameters that are set in the algorithm before the training process begins. The threshold value in binary classification represents the minimum probability required for a sample to be classified as belonging to the positive class. Generally, the default threshold for algorithms is set at 0.5. However, this default threshold may not yield optimal performance for models trained on imbalanced datasets.The best performing machine learning model achieved an accuracy of 98.48%. It also showed high precision and recall for the stable and unstable classes, with 94% for stable class and 98% for unstable system. These results were further validated using a Genetic algorithm, which mimicking the natural selection and evolution process to identify the most effective machine learning algorithm for our task.The results generated by the model will soon be accessible to the public through a web interface.