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Deep Learning Method Based on Two-Grid for Solving Stationary Partial Differential Equations
Journal of Xinjiang University(Natural Science Edition in Chinese and English) 2022, 39(4): 412-420
Published: 01 July 2022
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With the progress of machine learning in many fields, physics-informed neural networks provide new ideas for solving partial differential equations, but this method is difficult to obtain high-precision numerical solutions. Absorbing the philosophy of physics-informed neural network and the two-grid solution of partial differential equations, this paper puts forward the deep learning method based on two-grid for solving stationary partial differential equations. For the neural network to solve the multi-objective problem, the dynamic weight strategy is adopted to balance the numerical difference between the items in the loss function, and alleviate the gradient ill-conditioned phenomenon. Finally, this paper gives several numerical experiments to verify the effectiveness of the deep learning method combined with dynamic weight strategy in improving the calculation accuracy.

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