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 in order to guide and prioritize observational campaigns aiming at discovering some types of planets, as Earth-like planets. Our goal is to develop a generative model which is 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 large number of synthetic planetary systems with little computational cost, that can be used, for example, to guide observational campaigns. Our generative model is based on the transformer architecture which is well-known to efficiently capture correlations in sequences and is at the basis of all modern Large Language Models. To assess the validity of the generative model, we perform visual and statistical comparisons, as well as a machine learning driven tests. Finally, as a use case example, we consider the TOI-469 system, in which we aim at predicting the possible properties of planets c and d, based on the properties of planet b (the first that has been detected). We show using different comparison methods that the properties of systems generated by our model are very similar to the ones of the systems computed directly by the Bern model. We also show in the case of the TOI-469 system, that using the generative model allows to predict the properties of planets not yet observed, based on the properties of the already observed planet. We provide our model to the community on our website www.ai4exoplanets.com.

Searching for planets analogous to Earth in terms of mass and equilibrium temperature is currently the first step in the quest for habitable conditions outside our Solar System and, ultimately, the search for life in the universe. Future missions such as PLATO or LIFE will begin to detect and characterise these small, cold planets, dedicating significant observation time to them. The aim of this work is to predict which stars are most likely to host an Earth-like planet (ELP) to avoid blind searches, minimises detection times, and thus maximises the number of detections. Using a previous study on correlations between the presence of an ELP and the properties of its system, we trained a Random Forest to recognise and classify systems as 'hosting an ELP' or 'not hosting an ELP'. The Random Forest was trained and tested on populations of synthetic planetary systems derived from the Bern model, and then applied to real observed systems. The tests conducted on the machine learning (ML) model yield precision scores of up to 0.99, indicating that 99% of the systems identified by the model as having ELPs possess at least one. Among the few real observed systems that have been tested, 44 have been selected as having a high probability of hosting an ELP, and a quick study of the stability of these systems confirms that the presence of an Earth-like planet within them would leave them stable. The excellent results obtained from the tests conducted on the ML model demonstrate its ability to recognise the typical architectures of systems with or without ELPs within populations derived from the Bern model. If we assume that the Bern model adequately describes the architecture of real systems, then such a tool can prove indispensable in the search for Earth-like planets. A similar approach could be applied to other planetary system formation models to validate those predictions.

Constraining planet formation models based on the observed exoplanet population requires generating large samples of synthetic planetary systems, which can be computationally prohibitive. A significant bottleneck is simulating the giant impact phase, during which planetary embryos evolve gravitationally and combine to form planets, which may themselves experience later collisions. To accelerate giant impact simulations, we present a machine learning (ML) approach to predicting collisional outcomes in multiplanet systems. Trained on more than 500,000 $N$-body simulations of three-planet systems, we develop an ML model that can accurately predict which two planets will experience a collision, along with the state of the post-collision planets, from a short integration of the system's initial conditions. Our model greatly improves on non-ML baselines that rely on metrics from dynamics theory, which struggle to accurately predict which pair of planets will experience a collision. By combining with a model for predicting long-term stability, we create an efficient ML-based giant impact emulator, which can predict the outcomes of giant impact simulations with a speedup of up to four orders of magnitude. We expect our model to enable analyses that would not otherwise be computationally feasible. As such, we release our full training code, along with an easy-to-use API for our collision outcome model and giant impact emulator.

This paper presents a learning system architecture, Memory Mosaics, in which multiple associative memories work in concert to carry out a prediction task of interest. Such systems are closely related to memory networks [Weston et al., 2014, Sukhbaatar et al., 2015] and resemble transformers [Vaswani et al., 2017] despite significant differences. Like transformers, Memory Mosaics possesses some of the disentanglement and compositional capabilities that have long eluded machine learning systems [Lake and Baroni, 2018]. Unlike transformers whose internal mechanism are hard to decipher [Olsson et al., 2022, Bietti et al., 2024], Memory Mosaics achieve these capabilities in comparatively transparent ways. The three main contributions of this work are (a) recognizing and exploiting a similarity between smoothing associative memories and self-attention, (b) identifying and illustrating the predictive disentanglement principle which explains how training decomposes the overall task in interesting ways, and (c) showing that this comparatively transparent architecture matches the performance of decoding transformers on a language modeling task. Section 2 describes the basic architecture and outlines its consequences. Section 3 illustrates the predictive disentanglement principle. Section 4 extends these ideas to fully formed memory mosaics.

The transit method allows the detection and characterization of planetary systems by analyzing stellar light curves. Convolutional neural networks appear to offer a viable solution for automating these analyses. In this research, two 1D convolutional neural network models, which work with simulated light curves in which transit-like signals were injected, are presented. One model operates on complete light curves and estimates the orbital period, and the other one operates on phase-folded light curves and estimates the semimajor axis of the orbit and the square of the planet-to-star radius ratio. Both models were tested on real data from TESS light curves with confirmed planets to ensure that they are able to work with real data. The results obtained show that 1D CNNs are able to characterize transiting exoplanets from their host star's detrended light curve and, furthermore, reducing both the required time and computational costs compared with the current detection and characterization algorithms.

The transit method is one of the most relevant exoplanet detection techniques, which consists of detecting periodic eclipses in the light curves of stars. This is not always easy due to the presence of noise in the light curves, which is induced, for example, by the response of a telescope to stellar flux. For this reason, we aimed to develop an artificial neural network model that is able to detect these transits in light curves obtained from different telescopes and surveys. We created artificial light curves with and without transits to try to mimic those expected for the extended mission of the Kepler telescope (K2) in order to train and validate a 1D convolutional neural network model, which was later tested, obtaining an accuracy of 99.02 % and an estimated error (loss function) of 0.03. These results, among others, helped to confirm that the 1D CNN is a good choice for working with non-phased-folded Mandel and Agol light curves with transits. It also reduces the number of light curves that have to be visually inspected to decide if they present transit-like signals and decreases the time needed for analyzing each (with respect to traditional analysis).

Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural Networks (ANNs) to replace expensive parts of the integration of planetary systems. Neural networks that include physical knowledge have grown in popularity in the last few years, although few attempts have been made to use them to speed up the simulation of the motion of celestial bodies. We study the advantages and limitations of using Hamiltonian Neural Networks to replace computationally expensive parts of the numerical simulation. We compare the results of the numerical integration of a planetary system with asteroids with those obtained by a Hamiltonian Neural Network and a conventional Deep Neural Network, with special attention to understanding the challenges of this problem. Due to the non-linear nature of the gravitational equations of motion, errors in the integration propagate. To increase the robustness of a method that uses neural networks, we propose a hybrid integrator that evaluates the prediction of the network and replaces it with the numerical solution if considered inaccurate. Hamiltonian Neural Networks can make predictions that resemble the behavior of symplectic integrators but are challenging to train and in our case fail when the inputs differ ~7 orders of magnitude. In contrast, Deep Neural Networks are easy to train but fail to conserve energy, leading to fast divergence from the reference solution. The hybrid integrator designed to include the neural networks increases the reliability of the method and prevents large energy errors without increasing the computing cost significantly. For this problem, the use of neural networks results in faster simulations when the number of asteroids is >70.

Despite over three hundred years of effort, no solutions exist for predicting when a general planetary configuration will become unstable. We introduce a deep learning architecture to push forward this problem for compact systems. While current machine learning algorithms in this area rely on scientist-derived instability metrics, our new technique learns its own metrics from scratch, enabled by a novel internal structure inspired from dynamics theory. Our Bayesian neural network model can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short N-body time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on compact resonant and near-resonant three-planet configurations, the model demonstrates robust generalization to both non-resonant and higher multiplicity configurations, in the latter case outperforming models fit to that specific set of integrations. The model computes instability estimates up to five orders of magnitude faster than a numerical integrator, and unlike previous efforts provides confidence intervals on its predictions. Our inference model is publicly available in the SPOCK package, with training code open-sourced.

In the last two decades, since the first exoplanet has been discovered, scientists have identified more than 4000 planets orbiting other stars, of which half are in multi-planet systems. Out of these, at least 700 of them have planets which can be at potential risk of devastating collision. Researchers even believe that there are possibilities of many collisions that have already taken place that we are not aware of. Several questions, such as how planets organise themselves, prevent themselves from colliding into each other or how they remain stable have been the centre of research for many years. One of the requirements to be able to detect these are to make sure that a planetary system is stable.

While three planets have been detected in the Kepler-431 system, little is known about the shapes of their orbits. On the left are a large number of superimposed orbits for each planet that are consistent with observations. An international team of astrophysicists led by Princeton's Daniel Tamayo removed all the unstable configurations that would have already collided and couldn't be observed today. Doing this with previous methods would take over a year of computer time. With their new model SPOCK, it takes 14 minutes.