Nuclear Neural Networks: Emulating Late Burning Stages in Core-collapse Supernova Progenitors

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of fully coupled stiff ordinary differential equations, making the simulations computationally intensive and prone to numerical instability. To overcome this barrier, we design a nuclear neural network (NNN) framework with multiple hidden layers to emulate nucleosynthesis calculations and conduct a proof of concept to evaluate its performance. The NNN takes the temperature, density, and composition of a burning region as input and predicts the resulting isotopic abundances along with the energy generation and loss rates. We generate training sets for initial conditions corresponding to oxygen core depletion and beyond using large nuclear reaction networks, and compare the predictions of the NNNs to results from a commonly used small net. We find that the NNNs improve the accuracy of the electron fraction by 280%-660%, the average atomic and mass numbers by 150%-360%, and the nuclear energy generation by 250%-750%, consistently outperforming the small network across all time steps. They also achieve significantly better predictions of neutrino losses on relatively short timescales, with improvements ranging from 100% to 1,000,000%. While further work is needed to enhance their accuracy and applicability to different stellar conditions, integrating NNN-trained models into stellar evolution codes is promising for facilitating the large-scale generation of core-collapse supernova progenitors with higher physical fidelity.