Journal
COMMUNICATIONS IN THEORETICAL PHYSICS
Volume 73, Issue 1, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1572-9494/abc3ad
Keywords
sine-Gordon equation; deep residual network; soliton; integrable system
Categories
Funding
- National Natural Science Foundation of China [11675054]
- Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things [ZF1213]
- Science and Technology Commission of Shanghai Municipality [18dz2271000]
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The paper introduces a new architecture that combines deep residual neural networks with underlying physical laws to address unresolved issues in solving nonlinear evolution equations. By utilizing the sine-Gordon equation as a case study, the model demonstrates good numerical results and robustness against small perturbations.
Despite some empirical successes for solving nonlinear evolution equations using deep learning, there are several unresolved issues. First, it could not uncover the dynamical behaviors of some equations where highly nonlinear source terms are included very well. Second, the gradient exploding and vanishing problems often occur for the traditional feedforward neural networks. In this paper, we propose a new architecture that combines the deep residual neural network with some underlying physical laws. Using the sine-Gordon equation as an example, we show that the numerical result is in good agreement with the exact soliton solution. In addition, a lot of numerical experiments show that the model is robust under small perturbations to a certain extent.
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