Organizations: School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA, 30332, USA · Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA · School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA · Machine Learning Center, Georgia Institute of Technology, Atlanta, GA, 30332, USA
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. This approach is constructed using the Transformer-based architecture that can extract long-range interactions from TTV sequential data. We focus on two-planet systems based on Kepler-88 as a starting point, with the inner planet fixed to the properties of Kepler-88 and the mass and orbital elements of the outer planet varied. Applying to Kepler-88, we obtained an overall fractional error of ≲10% on semi-major axis and eccentricity, and ∼10−30% on planet mass (assuming that the stellar and transiting planet parameters are known), based on a training set of a million simulations. When applied to the test set, our model achieves low fractional errors of less than a few percent for systems with TTV semi-amplitudes ranging from ∼0.3 s to ∼5 min. Extending our approach to a broader range of planetary architectures, including systems with substantially weaker or stronger TTV signals and those containing additional planets or stellar companions, remains an important direction for future work.
Figures & tables
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 [ 10 ] . The system parameters are based on [ 38 ] , 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 [ 38 ] semi-major axis values. y-axis is χ2=∑abs(Vsim)(Vfixed−Vsim)2 , where Vfixed is the simulated TTV with fixed parameters based on [ 38 ] while Vsim represents the simulated TTV with varied semi-major axis.
Planet b
Planet c
Mass
8.7ME
10ME−10MJ
Semi-major axis a
0.095 AU
0.117 - 5 AU
Eccentricity e
0.05593
0.01 - 0.1
Inclination
0.945∘
lower bound - 7.7∘
Argument of Periastron
−179.41∘
0∘−360∘
Longitude of ascending node
270∘
0∘−360∘
Table 1: Summary of parameters of Kepler-88 System for N-body simulation
Figure 2: Fractional error distributions for predictions on the validation set using the pure Transformer, Transformer+LSTM, and Transformer+GRU architectures, shown in orange, green, and blue, respectively. The top-left panel shows the distribution for the semi-major axis ( a ), the top-right panel for the mass, the bottom-left panel for the eccentricity ( e ), and the bottom-right panel for the inclination (i). The MSE calculated on the validation set are 6.130×10−5 , 6.241×10−5 , and 2.475×10−3 , respectively for Transformer+GRU and Transformer+LSTM and pure Transformer.
Figure 3: Deep learning model architecture. NG and NF denotes the number of layers of GRU and FF, respectively. NT is the number of layers of transformer encoder. NFD is the number of FF layers in decoders. Token is an extra input of the transformer encoder, which is initialized as a tensor with zeros. There are three model variants in this work: the model with TDV input and without noise, the model without TDV input and without noise, and the model without TDV input and with noise. The numbers of layers, hidden dimensions, and other hyperparameters differ among these variants, as described in Sections II.3 and III.1 and implemented in the released code. As a representative example, for the model with TDV input and without noise, Input 1 has dimension [64,135,3] , corresponding to batch size, number of transit epochs, and the three input features: transit time, TTV, and TDV. Input 2 has dimension [64,1,2] . The GRU output has dimension [64,135,256] . After concatenating the GRU output, the encoded Input 2 token, and an additional zero token, the Transformer output has dimension [64,137,256] . The final output dimension is [64,4] .
Input
Model
a
Mass
e
i
GRIT
with TDV
0.1525 AU (0.3%)
176.4 ME (11.2%)
0.0628 (11.6%)
4.2∘ (9.9%)
Observation
with TDV
0.1468 AU
68.9 ME
0.0720
2.7∘
GRIT
without TDV
0.1419 AU (7.22%)
257.4 ME (29.5%)
0.0547 (2.81%)
Observation
without TDV
0.1539 AU
369.8 ME
0.0625
Table 2: Prediction on Kepler-88 without noise. The observation input is the transit information from [ 25 ] . For the input from GRIT, the parameters of a, mass, e and i based on [ 38 ] are 0.15292 AU, 198.8 ME , 0.05628, and 3.8∘ , respectively.
Input
a
Mass
e
GRIT
0.1454 AU (4.92%)
123.985 ME (37.6%)
0.0565 (0.403%)
Observation
0.1458 AU
194.9 ME
0.0410
Table 3: Prediction on Kepler-88 with noise. The observation input is the transit information from [ 25 ] . For the input from GRIT, the parameters of a, mass, e and i based on [ 38 ] are 0.15292 AU, 198.8 ME , 0.05628, and 3.8∘ , respectively.
Figure 4: Fractional error distributions on the testing set prediction for the model with TDV in the input. Top left shows the distribution for semi-major axis (a). Top right shows the distribution for the mass. Bottom left shows the distribution for the eccentricity (e). Bottom right shows the the distribution for the inclination (i).
Figure 5: Fractional error distributions on the testing set for the model without TDV in the input. From left to right, it shows the distribution for semi-major axis (a), mass, and eccentricity (e), respectively.
Figure 6: The relationship between the true value and the fractional error by the model with TDV. Each dot shows the fractional error for a specific system.
Figure 7: The relationship between the true value and the fractional error by the model without TDV. Each dot shows the fractional error for a specific system.
Figure 8: The fractional error versus the TTV semi-amplitude. Each dot shows the fractional error for a specific system. The orange dash-dotted line shows the running 90th percentile, and the red line shows the running median. The fractional error are typically low ≲ a few percent for a wide range of TTV semi-amplitude of ∼10−4−0.1 hr.
∼ 3AU, ∼ 1 MJ
∼ 3AU, ∼ 5 MJ
∼ 0.2 AU, ∼ 20 ME
a
T
3.0255 AU
2.9932 AU
0.1782 AU
P
3.0155 AU
2.9770 AU
0.1971 AU
FE
0.3305%
0.5441%
10.5684%
Mass
T
0.9924 MJ
4.9825 MJ
17.7183 ME
P
0.9901 MJ
4.9770 MJ
24.0963 ME
FE
0.2348%
0.1111%
35.9967%
Table 4: Prediction on selected example systems from testing set. T denotes true value, P represents prediction, and FE is the abbreviation of fractional error.
∼ 3AU, ∼ 1 MJ
∼ 3AU, ∼ 5 MJ
∼ 0.2 AU, ∼ 20 ME
a
T
3.0255 AU
2.9932 AU
0.1782 AU
P
3.0263 AU
3.0044 AU
0.2111 AU
FE
0.0277%
0.3742%
18.4295%
Mass
T
0.9924 MJ
4.9825 MJ
17.7183 ME
P
1.0081 MJ
4.9337 MJ
30.3714 ME
FE
1.5827%
0.9792%
71.4125%
Table 5: Prediction on selected example systems from testing set. T denotes true value, P represents prediction, and FE is the abbreviation of fractional error.
I present EXOVEIL, a transit detection system that learns what a star's brightness should look like and flags when reality disagrees. Unlike existing systems that require phase-folded input, EXOVEIL operates on raw flux time series and can detect planets that transit only once.A Transformer world model, trained on 16,499 Kepler light curves with transit-masked self-supervised learning, predicts expected stellar flux. A matched-filter detector with variance weighting extracts transit signals from the prediction residuals. A learned classifier (XGBoost) separates planets from false positives, achieving AUC 0.938 on Kepler DR25. Applied to single-transit injection-recovery, EXOVEIL recovers 32% of transits at 1000 ppm depth a task where all classification-based systems score 0% by construction. A blind search of 3,737 Kepler stars yields 179 new transit-like signals not present in the DR25 TCE catalogue, including 46 monotransit candidates. Applied withoutretraining to 47 confirmed TESS planets in the PLATO LOPS2 field, EXOVEIL achieves 100% recovery, demonstrating zero-shot cross-mission transfer. At PLATO's 25-second cadence, detection reaches 100 ppm -- approaching the Earth-analog regime. I provide the first application of conformal prediction to transit detection (95.9% empirical coverage) and release the system as pip install exoveil with pretrained weights and a candidate catalogue.
The discovery of exoplanets at scale has become one of the defining data science challenges in modern astrophysics. NASA's Transiting Exoplanet Survey Satellite (TESS) had catalogued over 7,800 planet candidates by early 2026, yet confirmation stands at fewer than 720. This paper introduces ExoNet, a multimodal deep learning framework that jointly processes phase-folded global and local light curve views alongside stellar parameter features through a calibrated late-fusion architecture combining 1D Convolutional Neural Networks, 8-head Multi-Head Attention over temporal feature maps, and a residual fusion head with post-hoc Temperature Scaling calibration. Trained on 7,585 labeled Kepler Objects of Interest, ExoNet achieves Test AUC = 0.9549 and 86.3% accuracy. Applied to 4,720 verified unconfirmed TESS Planet Candidates with TOI-TIC cross-identification verified against the NASA Exoplanet Archive, the model yields 1,754 high-confidence signals, 52 habitable-zone candidates, and six Earth-sized habitable-zone targets below 1.6 Earth radii. TOI-5728.01 and TOI-6716.01 emerge as the most Earth-like unconfirmed candidates. Full ablation confirms each modality improves AUC. Code and catalog are openly released.
Md. Rashadul Islam
Dept. of Computer Science and Engineering Daffodil International University Dhaka, Bangladesh
We present DEtection in phase-folded Light curves with cOntrastive Scoring (DELOS), a contrastive-learning-based framework designed to search for shallow transits in Kepler photometry. DELOS combines GPU-accelerated phase folding, optimized phase binning, and a custom one-dimensional convolutional encoder to assign a transit-likeness score to each folded light curve, thereby producing a score periodogram over trial periods without relying on pre-detected threshold-crossing events. Focusing on intermediate-to-long-period signals with orbital periods of 100-150 days, DELOS was trained on 20 million synthetic light curves generated with realistic transit models and Kepler-like noise properties, achieving a validation accuracy of 99.3 percent on the synthetic validation set. In controlled injection-recovery experiments, DELOS improves the combined precision-recall performance by 15.5 percent relative to Box-fitting Least Squares (BLS) and 11.25 percent relative to Transit Least Squares (TLS) in the low Signal-to-Noise Ratios (low-SNR) regime. It also accelerates the search by factors of approximately 3-5 and 74-80 compared with BLS and TLS, respectively. Applied to a selected Kepler validation sample, DELOS recovered all known shallow intermediate-to-long-period transit signals in the tested period range. These results demonstrate that DELOS provides an efficient and sensitive framework for low-SNR transit searches and represents a practical step toward future searches for longer-period terrestrial planets in Kepler, K2, TESS, PLATO, and Earth 2.0 data. Accordingly, this work is intended as a methodological development and validation study, with the detailed astrophysical validation of newly identified candidates deferred to future work.
Qingtian Liu, Jian Ge, XingChen Yan +4
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China · School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing 101408, China · Science Talent Training Center, Gainesville, FL, 32606 USA