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• W4313201314 abstract "We consider the modifications of a physics-informed neural network, based on conservation law constraint as the important feature of integrable physical models. This method implies introduction of the conservative properties of nonlinear physical systems into neural network to force qualitatively correctness of the solution during training. The conservation law constraint is put into neural network solver by adding the conserved quantity's residual to the loss function to train the neural network. We apply the modification on the one-dimensional nonlinear Schrӧdinger equation as the example of integrable system. In our experiments, Continuity Planes method was implemented to add the conservation constraint to the loss function. For further generalization on high dimension systems, we also considered Monte Carlo approach to control the conserved quantity through sum over interior points of the domain. The results obtained demonstrate an increase in the accuracy of prediction compared to conventional training for several cases." @default.
• W4313201314 created "2023-01-06" @default.
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• W4313201314 date "2022-01-01" @default.
• W4313201314 modified "2023-09-30" @default.
• W4313201314 title "Application of conservation laws to the learning of physics-informed neural networks" @default.
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• W4313201314 doi "https://doi.org/10.1016/j.procs.2022.11.030" @default.
• W4313201314 hasPublicationYear "2022" @default.
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