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DeepTTV: Deep Learning Prediction of Hidden Exoplanet From Transit Timing Variations

Chen Chen, Lingkai Kong, Gongjie Li, Molei Tao

TL;DR

The paper tackles the difficulty of recovering non-transiting companion parameters from transit timing variation data by replacing conventional Bayesian sampling with a data-driven, deep learning approach. It introduces a Transformer architecture with a GRU encoder to extract long-range information from TTV/TDV sequences and directly predict the mass, semi-major axis, eccentricity, and inclination of the unseen planet, using synthetic training data generated by GRIT N-body simulations. The authors assemble a large dataset (~1.85 million samples) by sampling parameters for the non-transiting planet, filtering to match observed transits, and evaluate the model on Kepler-88, achieving fractional errors around $2\%$ for mass and eccentricity. The work demonstrates rapid, MCMC-free inference for single-transit systems and highlights the potential of transformer-based architectures for hard inverse problems in exoplanet dynamics.

Abstract

Transit timing variation (TTV) provides rich information about the mass and orbital properties of exoplanets, which are often obtained by solving an inverse problem via Markov Chain Monte Carlo (MCMC). In this paper, we design a new data-driven approach, which potentially can be applied to problems that are hard to traditional MCMC methods, such as the case with only one planet transiting. Specifically, we use a deep learning approach to predict the parameters of non-transit companion for the single transit system with transit information (i.e., TTV, and Transit Duration Variation (TDV)) as input. Thanks to a newly constructed \textit{Transformer}-based architecture that can extract long-range interactions from TTV sequential data, this previously difficult task can now be accomplished with high accuracy, with an overall fractional error of $\sim$2\% on mass and eccentricity.

DeepTTV: Deep Learning Prediction of Hidden Exoplanet From Transit Timing Variations

TL;DR

The paper tackles the difficulty of recovering non-transiting companion parameters from transit timing variation data by replacing conventional Bayesian sampling with a data-driven, deep learning approach. It introduces a Transformer architecture with a GRU encoder to extract long-range information from TTV/TDV sequences and directly predict the mass, semi-major axis, eccentricity, and inclination of the unseen planet, using synthetic training data generated by GRIT N-body simulations. The authors assemble a large dataset (~1.85 million samples) by sampling parameters for the non-transiting planet, filtering to match observed transits, and evaluate the model on Kepler-88, achieving fractional errors around for mass and eccentricity. The work demonstrates rapid, MCMC-free inference for single-transit systems and highlights the potential of transformer-based architectures for hard inverse problems in exoplanet dynamics.

Abstract

Transit timing variation (TTV) provides rich information about the mass and orbital properties of exoplanets, which are often obtained by solving an inverse problem via Markov Chain Monte Carlo (MCMC). In this paper, we design a new data-driven approach, which potentially can be applied to problems that are hard to traditional MCMC methods, such as the case with only one planet transiting. Specifically, we use a deep learning approach to predict the parameters of non-transit companion for the single transit system with transit information (i.e., TTV, and Transit Duration Variation (TDV)) as input. Thanks to a newly constructed \textit{Transformer}-based architecture that can extract long-range interactions from TTV sequential data, this previously difficult task can now be accomplished with high accuracy, with an overall fractional error of 2\% on mass and eccentricity.
Paper Structure (3 sections, 1 figure)

This paper contains 3 sections, 1 figure.

Table of Contents

  1. Introduction
  2. Method
  3. Data Preparation

Figures (1)

  • Figure 1: How TTV changes as the semi-major axis varies. Peaks demonstrate the lack of regularity (i.e. smoothness) in the response. Results obtained from high accuracy N-body simulations grit. The system parameters are based on Nesvorny_2013, with the semi-major axis varying within $10\%$ of the given value of 0.15292 AU (1000 different values simulated), and other parameters fixed. x-axis is the difference between the tested and given Nesvorny_2013 semi-major axis values. y-axis is $\chi^2 = \sum \frac{(V_{fixed} - V_{sim})^2}{abs(V_{sim})}$, where $V_{fixed}$ is the simulated TTV with fixed parameters based on Nesvorny_2013 while $V_{sim}$ represents the simulated TTV with varied semi-major axis.