https://blog.tensorflow.org/2019/07/predicting-planets-from-orbital-deep-learning.html

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July 22, 2019 —
*A guest post by Kyle A. Pearson*

IntroductionIn the early 1700s, physicists and astronomers were eagerly testing the newly-discovered laws of gravitation by Isaac Newton and planetary motion by Johannes Kepler. The astronomers Urbain Le Verrier and John Couch Adams conducted multiple observations of Uranus in the 1700s to test the theories. They independently concluded that Uranus’ orbit was deviat…

Predicting planets from orbital perturbations using deep learning

This project is a winning submission to the #PoweredByTF 2.0 Challenge. A more detailed technical description of how TensorFlow is used for this project can be found in this publication. The sections below give a physical description of the training data and summarize how TensorFlow is used.

```
from nbody.simulation import generate, analyze, report
from nbody.tools import mjup,msun,mearth
if __name__ == "__main__":
# units: Msun, Days, au
objects = [
{'m':1.12},
{'m':0.28*mjup/msun, 'P':3.2888, 'inc':3.14159/2, 'e':0, 'omega':0 },
{'m':0.988*mjup/msun, 'P':7, 'inc':3.14159/2, 'e':0, 'omega':0 },
{'m':0.432*mjup/msun, 'P':12, 'inc':3.14159/2, 'e':0, 'omega':0 },
]
# year long integrations, timestep = 1 hour
sim_data = generate(objects, 365, 365*24)
# collect the analytics of interest from the simulation
ttv_data = analyze(sim_data)
# plot the results
report(ttv_data, savefile='report.png')
```

The code should produce an output like the figure below:The N-body model depends on, at least, a few parameters: mass of the star (M*), mass of the inner planet (M1), period of the inner planet (P1), mass of the outer planet (M2), period of the outer planet (P2), eccentricity of the outer planet (e2), and argument of periastron for the outer planet (w2). Typically, parameters pertaining to the star and inner planet are known ahead of time. Therefore, a machine learning algorithm using TensorFlow is designed to predict the parameters of the perturbing body (M2, P2, e2, w2) given the known parameters and the measured perturbation (i.e., O-C data). The neural network is a dual-input, multi-output regression model. The independent features (M*, M1, P1) are analyzed using a fully connected neural network while the time-dependent features are analyzed using a convolutional neural network. The output of each branch is then piped into a fully-connected neural network and finally, 4 parameters (M2, P2, e2, w2) are predicted. An example of the neural network architecture is shown below.

Training data is simulated in order to optimize the neural network for working with data from a particular telescope survey (e.g., TESS). The TESS mission is conducting an all-sky survey and will measure portions of the sky for as many as 180 days but also as little as 27 days depending on the RA and Dec. Research suggests at least 20 transit measurements are needed to derive a unique orbit solution. If we encounter real data outside of the training range, then we can simulate more data and retrain. After training the neural network, the error and sensitivity are characterized as a function of orbital period and companion mass. These errors are used to estimate the priors for a more rigorous Bayesian optimization to derive posteriors for the planetary parameters (see Figure).

- Analytic Light Curves for Planetary Transit Searches

- Mass and Orbit Determination from Transit Timing Variations of Exoplanets

- Searching for exoplanets using artificial intelligence

- Transiting Exoplanet Survey Satellite (TESS)

- Identifying Exoplanets with Deep Learning: A Five-planet Resonant Chain around Kepler-80 and an Eighth Planet around Kepler-90

- Evidence for 3 new multi-planet systems from TESS using a Bayesian N-body retrieval and machine learning

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Predicting planets from orbital perturbations using deep learning

July 22, 2019
—
*A guest post by Kyle A. Pearson*

IntroductionIn the early 1700s, physicists and astronomers were eagerly testing the newly-discovered laws of gravitation by Isaac Newton and planetary motion by Johannes Kepler. The astronomers Urbain Le Verrier and John Couch Adams conducted multiple observations of Uranus in the 1700s to test the theories. They independently concluded that Uranus’ orbit was deviat…

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