Physics Informed Neural Network Approach for Estimating the Coefficients of the Semi-Empirical Mass Formula

Abstract

Background: The Semi-Empirical Mass Formula (SEMF), also known as the Weizsacker formula, provides an approximate description of nuclear binding energy by incorporating volume, surface, Coulomb, asymmetry, and pairing effects within the liquid-drop model framework. Conventionally, the coefficients of the SEMF are determined using least-squares regression on experimental nuclear mass data.

Purpose: The purpose of this study is to develop and demonstrate a Physics-Informed Neural Networks (PINNs) framework for estimating the coefficients of the SEMF by embedding the nuclear-physics structure of the model directly into the learning process.

Methods: A physics-informed neural network was developed with the SEMF explicitly embedded in the loss function. Experimental nuclear mass data were used for training, while the SEMF coefficients were treated as trainable parameters. The model was optimized via c² minimization, measuring weighted squared deviations between experimental and predicted binding energies, with physically motivated bounds imposed to ensure stability and interpretability.

Results: The PINN framework successfully recovered physically meaningful values of the SEMF coefficients with improved numerical stability compared to conventional regression-based methods. The predicted binding energies exhibited strong agreement with experimental data across a wide range of nuclei. Incorporation of physical constraints significantly reduced overfitting and enhanced the generalization capability of the model.

Conclusion: This study demonstrates that Physics-Informed Neural Networks provide an effective and reliable framework for estimating the coefficients of the Semi-Empirical Mass Formula.