Neural network solver for nonlinear partial differential equations based on improved Euler method
To address the poor generalization performance of conventional deep learning methods in solving nonlinear partial differential equations,a long short-term convolutional recurrent neural network with an improved Euler method connected network module is proposed.The construction of the neural network employs the improved Euler method and finite difference method.Effective connections between the modules are realized through the improved Euler method.The derivative terms involved in the partial differential equation are accurately approximated by convolutions kernels constructed based on the finite difference method.Simulation experiments are conducted on two typical nonlinear partial differential equations,namely the Burgers equation and λ-ω reaction-diffusion equation.The experi-mental results prove that this method not only has high precision on the training data,but also shows strong generalization ability when extrapolating to new fields.
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