An international team at the GSI Helmholtz Centre for Heavy Ion Research and the Facility for Antiproton and Ion Research (FAIR) has built a machine learning system that sharply cuts the computing cost of simulating how the universe produces heavy elements. The model, published in Physical Review D, targets the rapid neutron capture process that drives element formation in neutron star mergers and supernovae.
The r-process and the computing bottleneck
Many heavy elements emerge from the r-process, a sequence where atomic nuclei grab free neutrons so quickly that some neutrons convert to protons, letting nuclei swell into heavier species. Modeling these reactions in full detail strains even the most advanced supercomputers. Researchers typically simplify the reaction networks to make simulations tractable, losing fidelity in the process.
"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," said Dr. Oliver Just, first author and a researcher in the Nuclear Astrophysics & Structure department at GSI/FAIR. "Our new model RHINE, which uses artificial intelligence, offers an efficient alternative."
How RHINE approximates nuclear heating
The system, called RHINE (r-process heating implementation in hydrodynamic simulations with neural networks), trains a deep neural network to estimate heating rates-the energy released during nuclear reactions-while hydrodynamic simulations run. Heating shapes how matter is ejected in stellar explosions and influences the light curves observed as kilonovae.
Instead of solving every nuclear equation in real time, the AI learns from a library of reference calculations that include complete reaction networks. "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," explained Dr. Zewei Xiong, a scientist in the same GSI/FAIR department and a key developer of the machine learning models.
Validation and what comes next
The team compared RHINE's predictions against reference data and found high agreement. "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," Xiong said. "We also deduced from the results that r-process heating is an important effect that should be better accounted for in future modeling."
The researchers have made the RHINE source code publicly available, and they say the approach could enable much finer-grained simulations of neutron star mergers and supernovae. Those improved models may eventually bridge experiments at the upcoming FAIR facility with astronomical observations of stellar explosions. The project was co-funded by the European Research Council and other organizations.
Why this matters for science and research professionals
For researchers in nuclear astrophysics, computational physics, and adjacent fields, RHINE demonstrates a practical path to embedding trained neural networks into large-scale hydrodynamic simulations. The model replaces a computationally intensive sub-process with a validated surrogate, freeing resources for higher-resolution physics or faster parameter sweeps. The open-source release means teams can adapt the method to their own simulation codes without starting from scratch.
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