Taming Nuclear Complexity with a Committee of Multilayer Neural Networks

We demonstrate that a committee of deep neural networks is capable of predicting the ground-state and excited energies of more than 1800 atomic nuclei with an accuracy akin to the one achieved by state-of-the-art nuclear energy density functionals (EDFs) and with significantly less computational cost. An active learning strategy is proposed to train this algorithm with a minimal set of 210 nuclei. This approach enables future fast studies of the influence of EDF parametrizations on structure properties over the whole nuclear chart and suggests that for the first time a machine learning framework successfully encoded several correlated aspects of nuclear deformation.

Figure 1

rms of the HFB energy on the test nuclei as a function of the size of the training set (in percent of the AMEDEE database). We compare results obtained with a training set determined by the active learning (red), by random sampling (black), and by an incremental choice based on the test loss (green).

Figure 2

(a) The AMEDEE database nuclei are plotted in gray as a function of $N$ and $Z$. The red squares stand for nuclei included in the 10% training set obtained by the active learning. Panels (b)–(d) display the resulting AI versus HFB root mean square per nucleus [${\mathcal{L}}_t^{1/2}(N,Z)$] for the three outputs $E_{\mathrm{HFB}}$, ${\mathcal{I}}_2$, and ${\mathit{B}}_{00}$, respectively.

Figure 3

HFB energy (a), rotational inertia along the principal axis (b), and vibrational inertia related to elongation (c) resulting from both constrained HFB calculations and the AI. These functions are plotted for ${}^{178}\mathrm{Os}$ in the standard polar representation where $\beta$ is the radial coordinate and $\gamma$ the polar angle.

Figure 4

Excitation spectrum of ${}^{178}\mathrm{Os}$ obtained from both the AI (AI) and the constrained HFB calculations (HFB). The experimental spectrum (Exp.), taken from the ENSDF database [36], is also displayed.