Journal
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
Volume 68, Issue 9, Pages 6725-6733Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAP.2020.2985172
Keywords
Computational modeling; Mathematical model; Permittivity; Poisson equations; Machine learning; Convolutional neural networks; Two dimensional displays; Convolutional neural network (ConvNet); deep learning; finite-difference method (FDM); learning capacity; Poisson's equation
Funding
- National Science Foundation of China [61571264, 61971263]
- National Key Research and Development Program of China [2018YFC0603604]
- Guangzhou Science and Technology Plan [201804010266]
- Beijing Innovation Center for Future Chip
- Research Institute of Tsinghua, Pearl River Delta
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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.
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