The heaviest elements in the universe — the gold in a wedding ring, the uranium in reactor fuel — are not made in ordinary stars. They are assembled in rare, violent events such as the collision of two neutron stars or the explosion of a dying star, where matter is squeezed and heated until atomic nuclei can swallow free neutrons in quick succession. Modeling that process in detail has long strained even the largest supercomputers. A team at the GSI/FAIR laboratory in Germany now reports a way to make those simulations dramatically cheaper, replacing the most expensive step with a trained neural network.
The work, published in Physical Review D, centers on a tool the researchers call RHINE, short for "r-process heating implementation in hydrodynamic simulations with neural networks." The r-process — rapid neutron capture — is the chain of reactions responsible for most elements heavier than iron. As nuclei absorb neutrons and some of those neutrons decay into protons, the reactions release energy. That heat is not a minor detail: it shapes how fast the debris flies outward and how brightly the aftermath glows, including the kilonova that astronomers can see following a neutron-star merger.
Learning the physics instead of recomputing it
"Modeling all parameters requires incredible computing power, which is why the models often have to be simplified," said Dr. Oliver Just, the study's first author. Rather than solve the full nuclear network at every step of a simulation, RHINE learns from it. The team first ran a large library of complete reference calculations, then trained deep-learning models to reproduce the heating rates those calculations produce.
"With detailed comparisons, we validated our ML scheme against reference data," said Dr. Zewei Xiong, who led the design of the models. "The high degree of agreement suggests that the use of ML models can save a tremendous amount of computing time." The exercise also confirmed that r-process heating matters enough that future models should not leave it out.
The researchers, who also include Gabriel Martínez-Pinedo, have released the RHINE source code publicly and note the project was co-funded by the European Research Council. In the longer run, they hope faster simulations will help connect measurements from the future FAIR accelerator to what telescopes actually observe when stars tear themselves apart.