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超重核的裂变势垒高度和基态结合能是影响熔合反应中存活概率的关键物理量, 其准确性是存活概率计算中不确定性的主要来源. 本工作应用迁移学习技术来训练神经网络模型, 通过结合理论模型预测数据和实验数据, 改进了有限程液滴模型(FRLDM)和WS4理论模型对裂变势垒高度的预测. 结果显示, FRLDM模型的均方根误差从1.03 MeV降低到0.60 MeV, WS4模型的均方根误差从0.97 MeV降低到0.61 MeV. 对于结合能, 本文优化了AME2020的实验值与WS4理论预测之间的差值. 在测试集上, 均方根误差从0.33 MeV降低到0.17 MeV, 而在整个数据集上, 其从0.29 MeV降低到0.26 MeV. 本研究为提高裂变势垒高度和结合能预测的准确性提供了一种具有前景的方法, 这将有助于提高核反应存活概率计算的精度. 本文数据集可在
https://www.doi.org/10.57760/sciencedb.28388 中访问获取.This study uses machine learning, specifically transfer learning with neural networks, to improve the predictions of fission barrier heights and ground state binding energies of superheavy nuclei, which are crucial for calculating survival probabilities in fusion reactions. Transfer learning for neural networks involve two stages: pre-training and fine-tuning, each utilizing a distinct pre-training dataset and target dataset. In this work, we split the pre-training data into 60% for training and 40% for validation, while the target data are partitioned into 20% for test, with the remaining 80% further divided into 60% for training and 40% for validation. To construct the neural-network model, we adopt the proton number Z and mass number A as the input layer, employ two hidden layers, each containing 128 neurons with rectified linear unit (ReLU) activation, and set the learning rate to 0.001. For the fission-barrier-height model, the pre-training dataset is either the FRLDM or the WS4 model data, with the experimental measurements serving as the target set. For the ground-state binding-energy model, we first calculate the residuals between WS4 predictions and the AME2020 evaluation, then divide these residuals into a light-nucleus subset and a heavy-nucleus subset according to proton number. The light-nucleus subset is used for pre-training, and the heavy-nucleus subset for fine-tuning. After optimization, the root-mean-square error (RMSE) of the FRLDM barrier model decreases from 1.03 MeV to 0.60 MeV, and that of the WS4 barrier model drops from 0.97 MeV to 0.61 MeV. For the binding-energy model, the RMSE decreases from 0.33 MeV to 0.17 MeV on the test set and from 0.29 MeV to 0.26 MeV on the full data set. We also present the performances of the fission-barrier model before and after refinement, together with the predicted barrier heights along the isotopic chains of the new elements Z = 119 and Z = 120, and analyze the reasons for the differences in the results obtained by different models. We hope that these results will serve as a useful reference for future theoretical studies. The datasets in this paper are openly available at https://www.doi.org/10.57760/sciencedb.28388 .
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Keywords:
- fission barriers /
- binding energies /
- machine learning /
- superheavy nuclei
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图 1 测试集中裂变势垒高度Bf的实验值和理论估算值的比较. 蓝色圆圈代表实验结果, 红色正方形表示FRLDM或WS4的结果, 紫色三角形表示在不同理论模型(FRLDM 或 WS4)的数据集上预训练的神经网络模型的结果
Fig. 1. Comparison of experimental and theoretical estimates of the fission barrier Bf in the test set. Blue circles represent experimental results, red squares indicate the results from FRLDM or WS4, and purple triangles show the results from neural network models pre-trained on datasets of different theoretical models (FRLDM or WS4).
图 2 由FRLDM和WS4提供的测试数据在优化前后的均方根误差
Fig. 2. The root mean square error (RMSE) of the test data provided by FRLDM and WS4 before and after optimization.
图 3 由FRLDM, ANNF, WS4和ANNW对预训练数据集估计的裂变势垒Bf的等值线图
Fig. 3. Contour plots of the fission barrier Bf estimated by FRLDM, ANNF, WS4, and ANNW for the pre-trained datasets.
图 4 WS4模型在测试集数据以及全部数据上优化前后的均方根误差
Fig. 4. Root mean square error of the WS4 model on the test dataset and the entire dataset before and after optimization.
表 1 测试集数据的裂变势垒高度(单位: MeV)与其他理论评估及实验数据[31]的比较
Table 1. Comparison of fission barriers (in MeV) for the test set data with other theoretical evaluations and experimental data[33].
核素 质子数 质量数 实验值 FRLDM ANNF WS4 ANNW 207Po 84 207 19.3 20.0 19.5 18.47 19.24 208Po 84 208 19.9 20.8 20.5 19.92 20.36 212Po 84 212 19.6 20.2 20.7 20.95 20.90 227Ac 89 227 7.40 6.98 8.37 7.16 7.44 233Th 90 233 6.65 5.47 6.24 6.95 6.96 239U 92 239 6.00 6.21 5.94 5.50 6.17 236Np 93 236 5.40 4.81 4.88 4.98 5.34 237Np 93 237 5.40 4.94 5.03 4.95 5.43 242Pu 94 242 5.05 6.41 5.88 6.19 5.56 243Pu 94 243 5.45 6.66 5.45 6.59 5.66 240Am 95 240 6.00 6.12 5.23 4.72 4.75 241Am 95 241 5.35 6.34 5.44 5.08 4.96 243Am 95 243 5.05 6.80 5.86 5.97 5.30 241Cm 96 241 5.50 6.32 5.23 4.68 4.54 248Cm 96 248 4.80 6.80 5.27 7.03 5.49 
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表 2 神经网络模型在(Z = 119, A = 293—299)以及(Z = 120, A = 294—302)的裂变势垒高度(以MeV为单位)以及结合能(以MeV为单位)的预言值
Table 2. Predicted fission barrier heights (in MeV) and binding energies (in MeV) for nuclides with Z = 119 and A = 293—299, as well as Z = 120 and A = 294—302, using neural network model.
质子数 质量数 ANNF ANNW ANNBinding 119 293 9.52 5.94 2060.78 119 294 9.91 6.00 2066.96 119 295 10.17 5.94 2074.71 119 296 10.41 5.87 2081.35 119 297 10.66 5.80 2088.92 119 298 10.91 5.73 2094.95 119 299 11.16 5.66 2102.11 120 294 9.35 5.98 2060.90 120 295 9.75 6.12 2067.63 120 296 10.14 6.23 2075.76 120 297 10.43 6.17 2082.32 120 298 10.68 6.10 2090.27 120 299 10.92 6.03 2096.30 120 300 11.17 5.96 2103.82 120 301 11.42 5.90 2109.78 120 302 11.66 5.83 2117.13
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