Speaker
Description
Background: The Semi-Empirical Mass Formula (SEMF), also known as the Weizsäcker 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 Network
(PINN) 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 constructed in which the SEMF was incorporated explicitly into the loss function. Experimental nuclear mass data were used as training inputs, while the SEMF coefficients were treated as trainable network parameters. The optimization was performed using 𝑐2 minimization, where the loss function quantified the weighted squared deviation between experimentally
measured and model-predicted binding energies. Physically motivated bounds were imposed on the coefficients 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.
