Predicting Nuclear Level Density Using a Physics-Informed Neural Network with Multi-Task Learning

The accurate determination of nuclear level density (NLD) is essential for a wide range of applications in nuclear science, including reactor design, nuclear astrophysics, and nuclear data evaluation. Traditional phenomenological models often face challenges in capturing key physical effects, such as collective excitations and shell structure, particularly in heavy and transitional nuclei, where the level density grows exponentially. Machine learning (ML) approaches have shown promise in improving predictive accuracy but are often limited by their purely data-driven nature, leading to challenges in interpretability and performance in regions with sparse experimental data. In this study, we propose a Physics-Informed Neural Network (PINN) framework, enhanced through multi-task learning (MTL), to address these limitations. The proposed model simultaneously predicts cumulative levels and mean resonance spacings by integrating experimental data with theoretical constraints, ensuring consistency with nuclear structure theory and robustness in extrapolating beyond the training data. Validation against both cumulative and yrast levels highlights the model’s ability to accurately capture rotational and vibrational excitations across a wide range of isotopes. Comparative evaluations demonstrate that the PINN model significantly outperforms traditional phenomenological models and purely data-driven approaches, offering a comprehensive and interpretable framework for advancing nuclear level density predictions and supporting practical applications in nuclear energy and astrophysics.