基于自编码器的贝叶斯神经网络用于基于模型的α粒子预形成因子描述
Bayesian neural network with autoencoder for model-based description of $α$-particle preformation factor
AI总结：
本研究提出基于贝叶斯神经网络与自编码器的混合框架，用于高精度描述α粒子预形成因子，并揭示了超重核的壳效应。
摘要：
α衰变是研究重核和超重核结构的重要探针，在其中α粒子预形成（P_α）是描述衰变半衰期的关键物理量。本工作开发了一种混合框架，将贝叶斯神经网络与自编码器（BNN-Auto）结合，与双曲势能（CPT）相结合，以系统地优化P_α的约束和预测。该模型采用变分推断对网络权重进行概率建模，自然地为预测提供稳健的不确定性量化，并利用自编码器增强特征表示的鲁棒性。基于535个核的数据，BNN-Auto方法在训练集上实现了P_α预测的均方根偏差（σ_RMS）的相对改进61.14%，在验证集上为54.49%。进一步分析发现，模型提取的P_α和半衰期在Z=86-90的同位素链和N=124-128和N=150-154的同位素中表现出显著的奇偶振荡和壳效应。此外，我们成功预测了Z=120核的α衰变半衰期，并观察到在N=184附近半衰期显著增加，这验证了预测的'稳定岛'的壳效应。本研究不仅为α衰变提供了高精度的理论描述，还为探索超重核结构提供了新的机器学习视角。
英文摘要：
$α$ decay is an important probe for studying the structure of heavy and superheavy nuclei, in which the $α$-particle preformation ($P_α$) is a key physical quantity for describing decay half-lives. This work develops a hybrid framework that integrates Bayesian neural networks with autoencoder (BNN-Auto), combined with the cosh potential (CPT), to systematically optimize the constraint and prediction of $P_α$. The model employs variational inference for probabilistic modeling of network weights, naturally providing robust uncertainty quantification for predictions, and utilizes an autoencoder to enhance the robustness of feature representation. Based on experimental data from 535 nuclei, the BNN-Auto method achieves relative improvements in the root mean square deviation ($σ_{\rm{RMS}}$) of $P_α$ prediction by $61.14\%$ on the training set and $54.49\%$ on the validation set. Further analysis reveals that the $P_α$ and half-life extracted by the model exhibit pronounced odd-even staggering and shell effects in isotopic chains with $Z=86-90$ and isotones with $N=124-128$ and $N=150-154$. Moreover, we successfully predict the $α$ decay half-lives of nuclei with $Z=120$ and observe a significant increase in the half-life near $N=184$, which verifies the shell effect of the predicted 'stable island'. This study not only provides a high-precision theoretical description for $α$ decay, but also offers a new machine learning perspective for exploring the structure of superheavy nuclei.
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