Accelerating stellar evolution models with neural networks, and application to the formation and evolution of astrophysical sources detected by LIGO/Virgo

Massive Stars Live in Pairs… Two major revolutions have transformed our understanding of stellar evolution. The first was the realization that most massive stars (over 75%) evolve within binary systems (Sana et al., 2012). This binarity has profound consequences on stellar evolution, significantly influenced by the presence of a companion, particularly through mass and angular momentum transfer (Chaty, 2022). The fate of these stellar pairs is dictated by the evolution of each component: the more massive star collapses first in a supernova explosion, giving birth to a neutron star or a black hole (Tauris et al., 2017). This process results in the formation of an accreting binary, where a compact object orbits its companion—one of the most fascinating objects in the Universe.

…and compact binaries eventually merge… The second revolution was the detection of gravitational waves by the LIGO-Virgo collaboration, originating from the merger of two black holes (first detected in September 2015) and later from two neutron stars (first detected in August 2017). These mergers occur at the final stage of binary evolution, depending on factors such as mass, orbital separation, and other key parameters (García et al., 2021). The merger of neutron stars is accompanied by electromagnetic radiation, producing a kilonova. Spectroscopic observations have, for the first time, unveiled the creation of heavy elements during such neutron star merger events, via the rapid nucleosynthesis process (r-process), confirming that it is a significant (even dominant?) source of galactic nucleosynthesis.

…impacting their environment. It is well established that the collapse of massive stars in supernovae plays a crucial role in enriching the interstellar medium—from heavy atoms to complex molecules—and triggering the formation of new stars. However, the long-term impact of massive stellar winds on their surroundings has long been overlooked. This ejected material disperses into the surrounding medium and may collide with dense interstellar clouds, potentially triggering the birth of new stars, as suggested by Herschel satellite observations (Chaty et al. 2012, Servillat et al. 2014).

The LIGO, Virgo, and KAGRA (LVK) gravitational-wave detectors are currently conducting their fourth observing campaign (O4, [link]), which is expected to result in an enriched catalog containing several hundred compact binary sources (mainly binary black holes). The significant increase—by a factor of 3 to 5—in the number of detections enables a deeper statistical analysis of the physical properties of the detected sources. By identifying homogeneous source populations, these analyses will provide answers to fundamental questions regarding the origin, formation mechanisms, and evolution of compact binaries observed by LVK.

A more accurate understanding of the evolution of compact binary systems relies on physical models. The modeling of these populations is based on stellar evolution simulations, performed using tools such as the MESA code [https://docs.mesastar.org]. Tracking the evolution of binaries, from their formation to the production of black holes or neutron stars, allow us to model the complex processes that transform a stellar binary into a compact binary (either black hole or neutron star). However, the inherent complexity of these simulations is enhanced by various phases of stellar evolution, which are determined by different key-parameters: accreting phase with stable transfer, common envelope phase with unstable transfer, mass loss through stellar winds, etc. This complexity results in an extremely high computational cost, limiting the ability to fully explore the parameter space of observed compact binaries, and to reproduce detected GW events. This is precisely the purpose of the POSYDON project [https://posydon.org], developed to aggregate and interpolate thousands of simulations, aiming at describing entire populations of sources rather than individual binaries. However, POSYDON currently relies on a rudimentary interpolation method that does not fully capture the complexity of the interactions and physical processes involved in binary evolution.

The objective of this PhD project is to explore more advanced regression techniques, and in particular using neural networks, to enhance the accuracy and efficiency of POSYDON’s population modeling.
This approach offers several advantages: on the one hand, increased precision thanks to the ability of neural networks to capture complex relationships; on the other hand, the development of a differentiable model that would facilitate the inference of initial binary properties from data observed by LVK. In this context, using neural networks to replace or enhance these interpolations appears to be a promising avenue. Neural networks can capture complex nonlinear relationships between stellar parameters, enabling more precise and generalizable modeling. Furthermore, a differentiable machine learning-based model would facilitate the inference of the initial conditions of binaries observed by LVK, thus improving our understanding of the formation channels of these sources. The application of artificial intelligence to the study of stellar evolution and compact binary evolution represents a major advancement, paving the way for faster and more precise analyses of future gravitational-wave detections by LVK, or even future GW detectors (ET, CE, etc).