Data-driven theoretical characterization of β-decay spectra in radioisotope energy materials via artificial fish swarm optimized adaptive kernel density estimation.

Introduction: Accurate modeling of beta-decay energy spectra is essential for theoretical analysis and performance optimization in radioisotope energy conversion. Conventional parameterization methods may introduce fitting bias, while fixed-bandwidth KDE lacks local adaptability for asymmetric, multi-peak and long-tailed spectral distributions. Methods: This study developed an Artificial Fish Swarm Algorithm-Adaptive Kernel Density Estimation (AFSA-AKDE) framework. After spectral data preprocessing, RMSE was used as the fitness function, the bandwidth was reformulated as an adaptive coefficient-controlled structure, and AFSA was used to optimize key parameters through foraging, swarming and following behaviors. Results: The method was validated using Ni-63, S-35 and C-14 samples with different thicknesses. For a 2 um Ni-63 sample, AFSA-AKDE achieved MAE = 0.0116%, RMSE = 0.0156% and R2 = 0.9998792. For a 0.2 um C-14 sample, it achieved MAE = 0.0158%, RMSE = 0.0243% and R2 = 0.996687. Discussion: Compared with fixed-bandwidth KDE, normal distribution models and recent adaptive KDE variants, AFSA-AKDE provides improved accuracy, stability and local adaptability for reconstructing complex beta-decay energy distributions.