A new penalty-free neural network method,PFNN-2,is presented for solving partial differential equations,which is a subsequent improvement of our previously proposed PFNN method[1].PFNN-2 inherits all advantages of PFN...A new penalty-free neural network method,PFNN-2,is presented for solving partial differential equations,which is a subsequent improvement of our previously proposed PFNN method[1].PFNN-2 inherits all advantages of PFNN in handling the smoothness constraints and essential boundary conditions of self-adjoint problems with complex geometries,and extends the application to a broader range of non-self-adjoint time-dependent differential equations.In addition,PFNN-2 introduces an overlapping domain decomposition strategy to substantially improve the training efficiency without sacrificing accuracy.Experiments results on a series of partial differential equations are reported,which demonstrate that PFNN-2 can outperform state-of-the-art neural network methods in various aspects such as numerical accuracy,convergence speed,and parallel scalability.展开更多
基金supported in part by National Natural Science Foundation of China(grants#12131002 and#12288101)Huawei Technologies Co.,Ltd.
文摘A new penalty-free neural network method,PFNN-2,is presented for solving partial differential equations,which is a subsequent improvement of our previously proposed PFNN method[1].PFNN-2 inherits all advantages of PFNN in handling the smoothness constraints and essential boundary conditions of self-adjoint problems with complex geometries,and extends the application to a broader range of non-self-adjoint time-dependent differential equations.In addition,PFNN-2 introduces an overlapping domain decomposition strategy to substantially improve the training efficiency without sacrificing accuracy.Experiments results on a series of partial differential equations are reported,which demonstrate that PFNN-2 can outperform state-of-the-art neural network methods in various aspects such as numerical accuracy,convergence speed,and parallel scalability.
