A transformer-based generative model for planetary systems

¹ Space Research and Planetary Sciences, Physics Institute, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
² Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
³ Institut für Planetenforschung, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

^★ Corresponding author.

Received: 18 September 2024
Accepted: 9 May 2025

Abstract

Context. Numerical calculations of planetary system formation are very demanding in terms of computing power. These synthetic planetary systems can, however, provide access to correlations, as predicted in a given numerical framework, between the properties of planets in the same system. Such correlations can, in return, be used to guide and prioritise observational campaigns aimed at discovering certain types of planets, such as Earth-like planets.

Aims. Our goal is to develop a generative model capable of capturing correlations and statistical relationships between planets in the same system. Such a model, trained on the Bern model, offers the possibility to generate a large number of synthetic planetary systems with little computational cost. These synthetic systems can be used, for example, to guide observational campaigns.

Methods. We used a training database of approximately 25 000 planetary systems, each with up to 20 planets and assuming a solar-type star, generated using the Bern model. Our generative model is based on the transformer architecture, which is well-known for efficiently capturing correlations in sequences and forms the basis of all modern large language models. To assess the validity of the generative model, we performed visual and statistical comparisons, as well as machine learning-driven tests. Lastly, as a use case, we considered the TOI-469 system, in which we aimed to predict the possible properties of planets c and d based on the properties of planet b, the first planet detected in the system.

Results. Using different comparison methods, we show that the properties of systems generated by our model are very similar to those of the systems computed directly by the Bern model. We also demonstrate that different classifiers cannot distinguish between the directly computed and generated populations, adding confidence that the statistical correlations between planets in the same system are similar. Lastly, we show in the case of the TOI-469 system that using the generative model allows us to predict the properties of planets not yet observed based on the properties of the already observed planet.

Conclusions. Our generative model, which we provide to the community on our website, can be used to study a variety of problems, such as understanding correlations between certain properties of planets in systems or predicting the composition of a planetary system given some partial information (e.g. the presence of some easier-to-observe planets). Nevertheless, it is important to note that the performance of our generative model relies on the ability of the underlying numerical model – here, the Bern model – to accurately represent the actual formation process of planetary systems. Our generative model could, on the other hand, very easily be retrained using as input other numerical models provided by the community.