Scientific result | Nuclear physics | Simulation ＆ modelling | Fundamental Research

# Simulating the behavior of nuclei with neural networks

*Published on 30 November 2020*

The structure of atomic nuclei continually defies understanding. However, it is possible to model it through the theoretical approach of "energy density functionals" (EDF), which presents the properties of nuclei in a complete and precise way. Specifically, EDFs describe the interactions between nucleons (neutrons and protons) as a function of the energy density of the system.

However, the deployment of EDFs on the scale of all the nuclei is limited by prohibitive computation times, especially in the case of systematic studies such as those required to study primordial nucleosynthesis. In order to go further, alternative computational approaches, using artificial intelligence in particular, have been proposed. Until now, they have had two major weaknesses as compared to EDFs: they require a large fraction of the available data for neural network training (80%), and they focus on a single experimental observable (mass or radius of the nucleus).

The CEA researchers therefore proposed a new approach: an algorithm that does not learn one observable but several "intermediate" measures calculated by EDF, such as the response of nuclei to deformations or vibrations. Moreover, since training is limited to 10% of the nuclei, the neural network itself determines (through "active learning") which nuclei provide it with the most information to accomplish its predictions.

For the first time, an algorithm consisting of a neural network committee was able to estimate the low-energy structure of all the nuclei, by training on only 210 nuclei, with a remarkable accuracy (less than 0.5% error on the energy of the fundamental states of osmium 178). After training, it can produce the whole set of results in just a few milliseconds, in comparison to the hundreds of hours of direct EDF computation (on all the nuclei). Therefore, it is now possible to perform only about 200 EDF calculations before being able to generalize the results of a functional on the whole nuclear chart, while maintaining a very good accuracy relative to the experiment.

This approach is already being implemented by a Franco-Belgian collaboration for the study of primordial nucleosynthesis as well as for the development of new, more complex EDF interactions. In addition, it is becoming possible to use neural networks for nuclear dynamics calculations, particularly fission.

Finally, the success of this approach is a first proof of principle that a neural network committee is capable of coding several correlated aspects of nuclear deformation. These networks probably possess a non-trivial internal representation of the physics of the system, the study of which could reveal new physical concepts.