Convolution-Based Model-Solving Method for Three-Dimensional, Unsteady, Partial Differential Equations.
- Resource Type
- Article
- Authors
- Zha, Wenshu; Zhang, Wen; Li, Daolun; Xing, Yan; He, Lei; Tan, Jieqing
- Source
- Neural Computation. Feb2022, Vol. 34 Issue 2, p518-540. 23p. 5 Diagrams, 11 Charts, 3 Graphs.
- Subject
- *PETRI nets
*MATHEMATICAL ability
*ALGORITHMS
- Language
- ISSN
- 0899-7667
Neural networks are increasingly used widely in the solution of partial differential equations (PDEs). This letter proposes 3D-PDE-Net to solve the three-dimensional PDE. We give a mathematical derivation of a three-dimensional convolution kernel that can approximate any order differential operator within the range of expressing ability and then conduct 3D-PDE-Net based on this theory. An optimum network is obtained by minimizing the normalized mean square error (NMSE) of training data, and L-BFGS is the optimized algorithm of second-order precision. Numerical experimental results show that 3D-PDE-Net can achieve the solution with good accuracy using few training samples, and it is of highly significant in solving linear and nonlinear unsteady PDEs. [ABSTRACT FROM AUTHOR]