Synthetic planetary systems can be generated either by solving differential equations (as in this paper, taking around 1000 CPU hours per model), or by training a generative model. In essence, this means considering planetary systems as sequences (e.g. ordered by increasing distance to their central star, but other ordering are possible) and computing the probability distribution of planet N, given the properties of planets 1 to N-1.

In this project (not published yet), we combine the strength of Recursive Neural Networks (RNN) to the representation power of mixture of Gaussians. We assume that the conditional probability of the properties of planet N given the properties of planets 1 to N-1 can be represented as a sum of Gaussians. Each Gaussian distribution is characterised by its co-variance matrix, its mean and its contribution to the total conditional probability (also called its weight). These parameters are predicted by training a RNN on a set of numerical simulations. The image below depicts the results we obtained assuming the conditional probability is the sum 5 gaussian distributions. The RNN has a hidden dimension of 128 and is made of two layers. As can be seen below, the distribution of generated and numerically simulated planets are similar, although the generative model has difficulties to generate the most massive planets.

This model has not been published yet, please contact us if you would like to develop this further, or apply to your own problem!

A comparison between results of numerical simulations (blue) and results of our generative model (RNN with mixture of Gaussian - orange). The x axis represents the distance between the central star and the planet (semi-major axis) in astronomical units (the distance between the Sun and the Earth) and in logarithmique scale. The vertical axis represents the mass of planets in Earth masses and in logarithmic scale. The Earth would be located at the (0,0) point on this diagram.