The Application of Machine Learning in Tidal Evolution Simulation of Star-Planet Systems

TL;DR

This work demonstrates that machine learning, specifically MLP regression and LightGBM classification, can meaningfully accelerate the exploration of tidal evolution in star-planet systems modeled with MESA. By training on large ensembles of simulated evolutions, the authors predict four key evolving quantities ($\log T_{\mathrm{eff}}$, $R_*$, $P_{\mathrm{rot}}$, $P_{\mathrm{orb}}$) and system ages with sub-percent median errors, while classifying planetary migration states with high accuracy. The approach yields speedups exceeding four orders of magnitude over direct model calculations, enabling rapid generation of complete evolutionary curves and extraction of migration-state features. Limitations include neglecting planetary magnetic fields and photoevaporation effects; nonetheless, the large ML-generated dataset and framework set the stage for scalable analysis of stellar-planet tidal interactions and their physical drivers.

Abstract

With the release of a large amount of astronomical data, an increasing number of close-in hot Jupiters have been discovered. Calculating their evolutionary curves using star-planet interaction models presents a challenge. To expedite the generation of evolutionary curves for these close-in hot Jupiter systems, we utilized tidal interaction models established on MESA to create 15,745 samples of star-planet systems and 7,500 samples of stars. Additionally, we employed a neural network (Multi-Layer Perceptron - MLP) to predict the evolutionary curves of the systems, including stellar effective temperature, radius, stellar rotation period, and planetary orbital period. The median relative errors of the predicted evolutionary curves were found to be 0.15%, 0.43%, 2.61%, and 0.57%, respectively. Furthermore, the speed at which we generate evolutionary curves exceeds that of model-generated curves by more than four orders of magnitude. We also extracted features of planetary migration states and utilized lightGBM to classify the samples into 6 categories for prediction. We found that by combining three types that undergo long-term double synchronization into one label, the classifier effectively recognized these features. Apart from systems experiencing long-term double synchronization, the median relative errors of the predicted evolutionary curves were all below 4%. Our work provides an efficient method to save significant computational resources and time with minimal loss in accuracy. This research also lays the foundation for analyzing the evolutionary characteristics of systems under different migration states, aiding in the understanding of the underlying physical mechanisms of such systems. Finally, to a large extent, our approach could replace the calculations of theoretical models.

Figures (11)

• Figure 1: The initial input parameter distributions are shown in the figure, where the initial semi-major axis of the planet is expressed in units of solar radii, and the initial stellar rotation frequency is expressed in units of solar rotation frequency.
• Figure 2: The number of samples in 6 subclass of (a) OUTG (b) OUTS (c) IN (d) OUTG DS (e) OUTS DS and (f) IN DS in training set and test set. The theoretical model calculates that only 3% of the samples exhibit double synchronization. Meanwhile, in Figure 6(a) of 2024MNRAS.529.2893G, it can be find that there are approximately 10 observed systems near $\Omega$/n=1. This indicates that the number of samples in double synchronization state is very low.
• Figure 3: The figure depicts six states of stellar migration: a. OUTG, b. OUTS, c. IN, d. OUTG DS, e. OUTS DS and f. IN DS.
• Figure 4: The figure illustrates the results of using NN for regression on stellar samples, including stellar effective temperature, stellar radius, and maximum main sequence age. Left Panel: the green dots represent the predicted values using the neural network model on the test set, the red dashed line represents the 45° line where predicted values are equal to true values. Middle Panel: The learning curve depicting the change in MAE (MSE) for the training and test sets during the learning process (recorded every 100 epochs, where the red and blue curves represent the training and test sets, respectively). Right Panel: the error distribution histogram of the predicted values and true values for the training set. The mean ($\mu$) and variance ($\sigma$) of the distribution are provided above each plot, and the black vertical lines indicate the percentiles (2nd, 16th, 50th, 84th, and 98th) of the samples. The top plot corresponds to stellar effective temperature, the middle plot represents stellar radius, and the bottom plot shows the maximum main sequence age of the stars.
• Figure 5: Similar to Figures \ref{['fig:regression1']}, we used NN regression on a star-planet system sample to predict the stellar rotation period, planetary orbital period, and maximum system age, with corresponding plots for each variable.