Emulation of the final r-process abundance pattern with a neural network

This work explores the construction of a fast emulator for the calculation of the final pattern of nucleosynthesis in the rapid neutron capture process (the $r$-process). An emulator is built using a feed-forward artificial neural network (ANN). We train the ANN with nuclear data and relative abundance patterns. We take as input the $\beta$-decay half-lives and the one-neutron separation energy of the nuclei in the rare-earth region. The output is the final isotopic abundance pattern. In this work, we focus on the nuclear data and abundance patterns in the rare-earth region to reduce the dimension of the input and output space. We show that the ANN can capture the effect of the changes in the nuclear physics inputs on the final $r$-process abundance pattern in the adopted astrophysical conditions. We employ the deep ensemble method to quantify the prediction uncertainty of the neutal network emulator. The emulator achieves a speed-up by a factor of about 20,000 in obtaining a final abundance pattern in the rare-earth region. The emulator may be utilized in statistical analyses such as uncertainty quantification, inverse problems, and sensitivity analysis.