A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems. (April 2023) - Yang, Yu; Gong, Helin; Zhang, Shiquan; Yang, Qihong; Chen, Zhang; He, Qiaolin; Li, Qing
Abstract: We put forward 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 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. Highlights: A DEPINN is proposed to solve neutron diffusion eigenvalue equations. An adaptive method with Adam and LBFGS is proposed to accelerate the convergence. Effect of parameters, samplings, loss function and generalization are investigated. Numerical results confirm the possibility of DEPINN for practical applications.