Modeling of the Forward Wave Propagation Using Physics-Informed Neural Networks

Alkhadhr, Shaikhah; Liu, Xilun; Almekkawy, Mohamed

doi:10.1109/ius52206.2021.9593574

Cited by 18 publications

(4 citation statements)

References 17 publications

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“…The ablation experiments compared the performance of deep neural network models introducing residual networks [9] and ODE-Net with traditional fully connected neural networks in solving partial differential equations. At the same time, this study also compared the performance of these deep learning models with classic numerical methods.…”

Section: Discussionmentioning

confidence: 99%

A numerical method to solve PDE through PINN based on ODENet

Wang

2024

ACE

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With the rapid development of articial intelligence, especially deep learning technology, scientic researchers have begun to explore its application in the eld of traditional scientic computing. Traditional scientic computing relies on mathematical equations to describe and predict the scientic laws of nature, while deep learning provides a new perspective to solve complex mathematical problems by learning patterns in data. The introduction of the Physical Information Neural Network (PINN) and the Ordinary Dierential Equation (ODENet) network layer enables deep learning technology to more accurately simulate and predict scientic phenomena. This study shows that by embedding an ODE-Net network layer in a physical information neural network (PINN), the tting accuracy and generalization performance of the model can be signicantly improved. Experimental results show that compared with traditional numerical methods and fully connected neural networks, this model combined with deep learning technology not only shows higher accuracy when solving partial dierential equations, but also exhibits faster convergence speed and stronger adaptability. These ndings not only promote the integration of scientic computing and deep learning, but also provide new research directions and practical strategies for using deep learning technology to solve complex scientic problems.

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Section: Discussionmentioning

confidence: 99%

A numerical method to solve PDE through PINN based on ODENet

Wang

2024

ACE

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“…Finally, DeepXDE is utilized for medical ultrasonography applications to simulate a linear wave equation with a single time-dependent sinusoidal source function [3], and the opensource library is also employed for the Buckley-Leverett problem [4]. A list of research publications that made use of DeepXDE is available online 1…”

Section: Deepxdementioning

confidence: 99%

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

et al. 2022

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Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

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“…Finally, DeepXDE is utilized for medical ultrasonography applications to simulate a linear wave equation with a single time-dependent sinusoidal source function (Alkhadhr et al, 2021), and the open-source library is also employed for the Buckley-Leverett problem (Almajid and Abu-Al-Saud, 2022). A list of research publications that made use of DeepXDE is available online 1 .…”

Section: Deepxdementioning

confidence: 99%