NUMERICAL SOLVER FOR COMPLEX REGIONAL PARTIAL DIFFERENTIAL EQUATIONS OF WATER POLLUTION DIFFUSION BASED ON DEEP NEURAL NETWORK

The complex regional Partial differential equation (PDE) is a common mathematical tool to control environmental pollution and forecast the weather. The traditional numerical solvers of the complex regional PDEs have difficulty in achieving accurate grid meshing. By virtue of its strong approximation ability, Deep neural networks (DNNs) are preferred for solving complex regional PDEs. This paper firstly summarises the weaknesses of traditional numerical methods, and then designs a DNN-based numerical solver for complex regional PDEs. The tests on two important PDEs show that the proposed solver is meshless and easy to implement, and achieves a high precision with a low computing complexity.