用于正演和反演 PDE 问题的深度模糊物理信息神经网络。

IF 6 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Neural Networks Pub Date : 2024-10-15 DOI:10.1016/j.neunet.2024.106750
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引用次数: 0

摘要

物理信息神经网络(PINNs)是一种独立于网格的偏微分方程(PDEs)求解方法,因其同时从数据和物理方程中学习的独特能力而备受关注。现有的 PINNs 方法总是假定数据是稳定可靠的,但从商业模拟软件中获得的数据往往不可避免地存在模糊和不准确的问题。显然,这将对使用 PINNs 解决正演和反演 PDE 问题产生负面影响。为了克服上述问题,本文提出了一种探索数据不确定性的深度模糊物理信息神经网络(FPINNs)。具体来说,为了捕捉数据背后的不确定性,FPINNs 通过模糊成员函数层和模糊规则层学习模糊表示。之后,我们使用深度神经网络来学习神经表征。随后,将模糊表示与神经表示进行整合。最后,物理方程的残差和数据误差被视为损失函数的两个分量,引导网络朝着遵循物理规律的方向进行优化,从而实现对物理场的精确预测。广泛的实验结果表明,在解决四个广泛使用的数据集上的正演和反演 PDE 问题时,FPINNs 优于这些比较方法。演示代码将在 https://github.com/siyuancncd/FPINNs 上发布。
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Deep fuzzy physics-informed neural networks for forward and inverse PDE problems
As a grid-independent approach for solving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have garnered significant attention due to their unique capability to simultaneously learn from both data and the governing physical equations. Existing PINNs methods always assume that the data is stable and reliable, but data obtained from commercial simulation software often inevitably have ambiguous and inaccurate problems. Obviously, this will have a negative impact on the use of PINNs to solve forward and inverse PDE problems. To overcome the above problems, this paper proposes a Deep Fuzzy Physics-Informed Neural Networks (FPINNs) that explores the uncertainty in data. Specifically, to capture the uncertainty behind the data, FPINNs learns fuzzy representation through the fuzzy membership function layer and fuzzy rule layer. Afterward, we use deep neural networks to learn neural representation. Subsequently, the fuzzy representation is integrated with the neural representation. Finally, the residual of the physical equation and the data error are considered as the two components of the loss function, guiding the network to optimize towards adherence to the physical laws for accurate prediction of the physical field. Extensive experiment results show that FPINNs outperforms these comparative methods in solving forward and inverse PDE problems on four widely used datasets. The demo code will be released at https://github.com/siyuancncd/FPINNs.
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来源期刊
Neural Networks
Neural Networks 工程技术-计算机:人工智能
CiteScore
13.90
自引率
7.70%
发文量
425
审稿时长
67 days
期刊介绍: Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.
期刊最新文献
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