Scientists have long known that the heaviest elements in the universe-gold, platinum, uranium-are forged in cataclysmic events like neutron star mergers. Simulating the rapid neutron-capture process that builds these elements has been limited by computing power. A team at GSI/FAIR and international collaborators has now built a machine learning model called RHINE that integrates directly into hydrodynamic simulations, cutting the computational cost of modeling the energy released during element formation. The work was published in Physical Review D.
Many elements heavier than iron are produced through the r-process, where atomic nuclei rapidly absorb free neutrons that later decay into protons. This occurs in environments with extreme neutron densities, such as merging neutron stars. The energy released during this process-known as r-process heating-can shape how material is ejected and influence the electromagnetic signals astronomers detect, including the kilonovae observed after mergers.
Training a neural network on nuclear reactions
"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 of the publication and researcher in the Nuclear Astrophysics & Structure department at GSI/FAIR.
The RHINE model-short for r-process heating implementation in hydrodynamic simulations with neural networks-sidesteps this bottleneck. The team first trained a deep learning neural network on a large set of reference calculations that used a complete set of nuclear reactions. Once trained, the model approximates heating rates during the r-process inside running hydrodynamic simulations with far less computational effort.
Validation shows strong agreement with reference data
Dr. Zewei Xiong, a scientist at GSI/FAIR who played a central role in designing the machine learning models, described the two-stage approach: "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."
The team validated RHINE against reference data and found a high degree of agreement. The results suggest that machine learning can save substantial computing time while preserving accuracy. The researchers also concluded that r-process heating has a stronger influence on ejecta dynamics than many previous simplified models accounted for, and should be included more carefully in future work.
Why this matters for science and research professionals
For researchers working at the intersection of simulation and experiment, RHINE demonstrates a practical pattern: replacing computationally expensive physics modules with trained neural networks that run inside existing simulation codes. This approach does not require rebuilding simulation frameworks from scratch. It points toward a method that could accelerate modeling pipelines across AI for Science & Research disciplines, from astrophysics to materials science, where the cost of first-principles calculations limits what can be studied. The team expects the technique to help connect upcoming experimental results from the FAIR facility with astronomical observations of stellar explosions and neutron star mergers.
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