Accurate estimation of nuclear masses and their prediction beyond the experimentally explored domains of the nuclear landscape are crucial to an understanding of the fundamental origin of nuclear properties and to many applications of nuclear science, most notably in quantifying the $r$-process of stellar nucleosynthesis. Neural networks have been applied with some success to the prediction of nuclear masses, but they are known to have shortcomings in application to extrapolation tasks. In this work, we propose and explore a novel type of neural network for mass prediction in which the usual neuron-like processing units are replaced by complex-valued product units that permit multiplicative couplings of inputs to be learned from the input data. This generalized network model is tested on both interpolation and extrapolation data sets drawn from the Atomic Mass Evaluation. Its performance is compared with that of several neural-network architectures, substantiating its suitability for nuclear mass prediction. Additionally, a prediction-uncertainty measure for such complex-valued networks is proposed that serves to identify regions of expected low prediction error.

翻译：核质量的精确估算及其在已实验探索的核景观范围之外的预测，对于理解核性质的根本起源以及核科学的众多应用（尤其是在量化恒星核合成的$r$过程中）至关重要。神经网络已在一定程度上成功应用于核质量预测，但已知其在处理外推任务时存在缺陷。本研究提出并探索了一种用于质量预测的新型神经网络，其中通常的类神经元处理单元被替换为复值乘积单元，从而允许从输入数据中学习输入之间的乘性耦合。该广义网络模型在取自原子质量评估的内插和外推数据集上进行了测试，并将其性能与多种神经网络架构进行了比较，证实了其适用于核质量预测。此外，针对此类复值网络提出了一种预测不确定性度量方法，有助于识别预期预测误差低的区域。