论文标题
具有数据启用物理信息的神经网络，具有有关解决中子扩散特征值问题的全面数值研究
A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems
论文作者
论文摘要
我们提出了一个具有数据启用物理信息的神经网络（DEPINN），并通过解决工业量表中子扩散特征值问题（NDEPS）进行了全面的数值研究。为了实现复杂工程问题的工程可接受的准确性，建议使用物理实验的少量先前数据，以提高培训的准确性和效率。我们使用Adam和LBFG设计了一种自适应优化程序，以在训练阶段加速收敛。我们讨论了不同的物理参数，采样技术，损耗函数分配以及所提出的DEPINN模型对解决复杂问题的概括性能的影响。在三个典型的基准问题（从简单的几何形状到复杂的几何形状，从单能方程到两组方程）上测试了提出的depinn模型的可行性。大量数值结果表明，depinn可以通过适当的优化程序有效地求解NDEP。一旦对其结构进行了训练，就可以将提出的销售概括为其他输入参数设置。这项工作证实了核反应堆物理学实用工程应用的可能性。
We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for complex engineering problems, a very small amount of prior data from physical experiments are suggested to be used, to improve the accuracy and efficiency of training. We design an adaptive optimization procedure with Adam and LBFGS to accelerate the convergence in the training stage. We discuss the effect of different physical parameters, sampling techniques, loss function allocation and the generalization performance of the proposed DEPINN model for solving complex problem. The feasibility of proposed DEPINN model is tested on three typical benchmark problems, from simple geometry to complex geometry, and from mono-energetic equation to two-group equations. Numerous numerical results show that DEPINN can efficiently solve NDEPs with an appropriate optimization procedure. The proposed DEPINN can be generalized for other input parameter settings once its structure been trained. This work confirms the possibility of DEPINN for practical engineering applications in nuclear reactor physics.
