Solving partial differential equation based on extreme learning machine

Abstract

In this paper, we present a novel learning method based on extreme learning machine algorithm called ELMNET for solving partial differential equations (PDEs). A loss function that relies on partial differential equation (PDE), initial and boundary condition (I/BC) residual was proposed. The proposed loss function is discretization-free and highly parallelizable. The network parameters are determined by solving a system of linear equations using the ELM algorithm. We demonstrated the performance of ELMNET in solving the advection–diffusion PDE (AD-PDE) as case-studies. The experimental results from the proposed method were compared to the efficient deep neural network and they showed that the ELMNET attains significant improvements in term of both accuracy and training time.