Approximation of functions from Korobov spaces by shallow neural networks

Liu, Yuqing; Mao, Tong; Zhou, Ding-Xuan

doi:10.1016/j.ins.2024.120573

Information Sciences

2024

DOI: 10.1016/j.ins.2024.120573

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Approximation of functions from Korobov spaces by shallow neural networks

Yuqing Liu,

Tong Mao,

Ding-Xuan Zhou

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2024

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Cited by 2 publications

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Gradient-enhanced fractional physics-informed neural networks for solving forward and inverse problems of the multiterm time-fractional Burger-type equation

Yuan,

Liu,

et al. 2024

MATH

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<p>In this paper, we introduced the gradient-enhanced fractional physics-informed neural networks (gfPINNs) for solving the forward and inverse problems of the multiterm time-fractional Burger-type equation. The gfPINNs leverage gradient information derived from the residual of the fractional partial differential equation and embed the gradient into the loss function. Since the standard chain rule in integer calculus is invalid in fractional calculus, the automatic differentiation of neural networks does not apply to fractional operators. The automatic differentiation for the integer order operators and the finite difference discretization for the fractional operators were used to construct the residual in the loss function. The numerical results demonstrate the effectiveness of gfPINNs in solving the multiterm time-fractional Burger-type equation. By comparing the experimental results of fractional physics-informed neural networks (fPINNs) and gfPINNs, it can be seen that the training performance of gfPINNs is better than fPINNs.</p>

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Approximation of functions from Korobov spaces by shallow neural networks

Cited by 2 publications

References 30 publications

Improved dendritic learning: Activation function analysis

Improved dendritic learning: Activation function analysis

Gradient-enhanced fractional physics-informed neural networks for solving forward and inverse problems of the multiterm time-fractional Burger-type equation

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