Learning nuclear cross sections across the chart of nuclides with graph neural networks

TL;DR

This paper demonstrates a deep learning framework combining representation learning and graph neural networks to predict nuclear cross sections across the chart of nuclides, revealing insights into nuclear structure and improving data interpolation.

Contribution

The work introduces a novel two-stage deep learning approach using VAEs or INRs with GNNs to predict nuclear cross sections and identify nuclear magic numbers, advancing nuclear data modeling.

Findings

Accurate cross section predictions within a 9x9 nuclear chart block.

VAE embeddings outperform in end-to-end training, INRs excel in latent space training.

The approach uncovers neutron magic numbers and enhances nuclear theory models.

Abstract

In this work, we explore the use of deep learning techniques to learn how nuclear cross sections change as we add or remove protons and neutrons. As a proof of principle, we focus on the neutron-induced reactions in the fast energy regime. Our approach follows a two-stage learning framework. First, we apply representation learning to encode cross section data into a latent space using either variational autoencoders (VAEs) or implicit neural representations (INRs). Then, we train graph neural networks (GNNs) on the resulting embeddings to predict missing values across the nuclear chart by leveraging the topological structure of neighboring isotopes. We demonstrate accurate cross section predictions within a 9x9 block of missing nuclei. We also find that the optimal GNN training strategy depends on the type of latent representation used, with VAE embeddings performing best under end-to-end optimization in the original space, while INR embeddings achieve better results when the GNN is trained only in the latent space. Furthermore, using clustering algorithms, we map groups of latent vectors into regions of the nuclear chart and show that VAEs and INRs can discover some of the neutron magic numbers. These findings suggest that deep-learning models based on the representation encoding of cross sections combined with graph neural networks holds significant potential in augmenting nuclear theory models, e.g., by providing reliable estimates of covariances of cross sections, including cross-material covariances.