论文 | Yu Yang, Helin Gong, Shiquan Zhang, Qihong Yang, Zhang Chen, Qiaolin He, Qing Li:A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems

本文（A data-enabled physics-informed neural network with comprehensive  numerical study on solving neutron diffusion eigenvalue problems）原载 Annals of  Nuclear Energy，由四川大学贺巧琳教授等科研人员创作，系四川大学智慧法治超前部署学科系列学术成果。后续会持续分享四川大学智慧法治超前部署学科系列学术成果，欢迎大家阅读。

Abstract:We put forward a data-enabled physics-informed neural network  1011 (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  eigenvalue problems. The feasibility of proposed DEPINN model is verified 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.

Yu Yang, Helin Gong, Shiquan Zhang, Qihong Yang, Zhang Chen, Qiaolin  He, Qing Li，A data-enabled physics-informed neural network with comprehensive  numerical study on solving neutron diffusion eigenvalue problems，Annals of  Nuclear Energy，183(2023):109656 .（论文下载）