Researchers at GSI/FAIR developed an AI-based simulation model named RHINE to model r-process heating in neutron star mergers. The findings were published in the journal Physical Review D on July 8, 2026.

The new system, RHINE, stands for r-process heating implementation in hydrodynamic simulations with neural networks. The model utilizes machine learning, specifically a deep learning neural network, to estimate energy released during nuclear reactions in the r-process while hydrodynamic simulations are running. This energy release, referred to as heating, influences the speed of ejected material and the light produced after stellar explosions.

Heavy atomic nuclei are formed during extreme cosmic phenomena like supernova explosions and neutron star mergers through a process called rapid neutron capture, or the r-process. During this process, atomic nuclei quickly absorb free neutrons. Some of these absorbed neutrons then transform into protons, leading to larger nuclei and the formation of heavy elements. The intense glow resulting from neutron star mergers is known as a kilonova.

Dr. Oliver Just, the study's first author and a researcher in the Nuclear Astrophysics & Structure department at GSI/FAIR, commented on the computational demands of modeling these events. "Researchers around the world strive to make these complex reactions understandable through theoretical simulations. However, modeling all parameters requires incredible computing power, which is why the models often have to be simplified," Just said. He added, "Our new model RHINE, which uses artificial intelligence, offers an efficient alternative."

The AI model is trained using an extensive library of reference calculations that include complete nuclear reaction networks. Dr. Zewei Xiong, a scientist in the same GSI/FAIR department, explained the training process. "First the ML models are trained using a large number of reference calculations produced with a full set of nuclear reactions. Subsequently, the models are adopted in running hydrodynamical simulations to approximate the heating rates during the r-process with minimal effort," Xiong said. He continued, "With detailed comparisons, we validated our ML scheme against reference data. The high degree of agreement suggests that the use of ML models can save a tremendous amount of computing time. We also deduced from the results that r-process heating is an important effect that should be better accounted for in future modeling."

The RHINE source code has been made publicly available. The European Research Council (ERC) co-funded the project. Oliver Just, Zewei Xiong, and Gabriel Martínez-Pinedo are credited as authors of the paper.