Deep learning

Physics

Mathematics

Poisson's equation

Poisson distribution

Algorithm

Statistics

Mathematical optimization

Reduction (mathematics)

Approximation error

Mathematical analysis

Parallel computing

Artificial intelligence

Programming language

Computational electromagnetics

Geometry

Electromagnetic field

Solver

Computer science

Computation

Quantum mechanics

Applied mathematics

Artificial neural network

Speedup

Convolutional neural network

IEEE Transactions on Antennas and Propagation

Fast and efficient computational electromagnetic simulation is a long-standing challenge. In this article, we propose a data-driven model to solve Poisson's equation that leverages the learning capacity of deep learning techniques. A deep convolutional neural network (ConvNet) is trained to predict the electric potential with different excitations and permittivity distribution in 2-D and 3-D models. With a careful design of cost function and proper training data generated from finite-difference solvers, the proposed network enables a reliable simulation with significant speedup and fairly good accuracy. Numerical experiments show that the same ConvNet architecture is effective for both 2-D and 3-D models, and the average relative prediction error of the proposed ConvNet model is less than 3% in both 2-D and 3-D simulations with a significant reduction in computation time compared to the finite-difference solver. This article shows that deep neural networks have a good learning capacity for numerical simulations. This could help us to build some fast solvers for some computational electromagnetic problems.

Study on a Fast Solver for Poisson’s Equation Based on Deep Learning Technique