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28 July 2023 Deep neural network Galerkin method for phase-field model
Xiaoyan Ge, Liang Ge
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Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 1275631 (2023) https://doi.org/10.1117/12.2686051
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China
Abstract
A Deep Neural Network Galerkin Method (DNNGM) is suggested in this paper to address the phase field system. Neural network approximation is utilized to obtain the solution. The neural network can reduce the amount of computation on account of meshless. The neural network is trained using randomly sampled time and space points. The stochastic gradient descent algorithm and minimization loss function are employed to fulfill the boundary and initial conditions, as well as the differential operators of the partial differential equations. Finally, numerical examples are utilized to verify the effectiveness of the algorithm.
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Xiaoyan Ge and Liang Ge "Deep neural network Galerkin method for phase-field model", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 1275631 (28 July 2023); https://doi.org/10.1117/12.2686051
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KEYWORDS
Neural networks
Deep learning
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