ArticleEntropy (Basel, Switzerland)2023
A Second-Order Network Structure Based on Gradient-Enhanced Physics-Informed Neural Networks for Solving Parabolic Partial Differential Equations.
Article in Entropy (Basel, Switzerland), 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Implementing physics-informed neural networks with deep learning for differential equations.Frontiers in artificial intelligence · 2026Article
- Research on temperature prediction model of molten steel of tundish in continuous casting.Scientific reports · 2024Article
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2 authors.
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Abstract
Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has successfully solved forward and inverse PDE problems. In this study, we considered a parametric light wave equation, discretized it using the central difference, and, through this difference scheme, constructed a new neural network structure named the second-order neural network structure. Additionally, we used the adaptive activation function strategy and gradient-enhanced strategy to improve the performance of the neural network and used the deep mixed residual method (MIM) to reduce the high computational cost caused by the enhanced gradient. At the end of this paper, we give some numerical examples of nonlinear parabolic partial differential equations to verify the effectiveness of the method.
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