DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations

Li, Ying; Xu, Longxiang; Ying, Shihui

doi:10.3390/math10121976

Cited by 11 publications

(5 citation statements)

References 57 publications

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“…This attribute makes it a powerful tool for analyzing local features [32]. Consequently, Li et al [33] developed a deep wavelet NN (DWNN) based on the PINNs approach. The employment of wavelets enables the extraction of multi-scale and detailed features, resulting in enhanced performance in solving PDEs.…”

Section: Wavelets and Cnnmentioning

confidence: 99%

Approximating Partial Differential Equations with Physics-Informed Legendre Multiwavelets CNN

Wang,

et al. 2024

Fractal Fract

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The purpose of this paper is to leverage the advantages of physics-informed neural network (PINN) and convolutional neural network (CNN) by using Legendre multiwavelets (LMWs) as basis functions to approximate partial differential equations (PDEs). We call this method Physics-Informed Legendre Multiwavelets CNN (PiLMWs-CNN), which can continuously approximate a grid-based state representation that can be handled by a CNN. PiLMWs-CNN enable us to train our models using only physics-informed loss functions without any precomputed training data, simultaneously providing fast and continuous solutions that generalize to previously unknown domains. In particular, the LMWs can simultaneously possess compact support, orthogonality, symmetry, high smoothness, and high approximation order. Compared to orthonormal polynomial (OP) bases, the approximation accuracy can be greatly increased and computation costs can be significantly reduced by using LMWs. We applied PiLMWs-CNN to approximate the damped wave equation, the incompressible Navier–Stokes (N-S) equation, and the two-dimensional heat conduction equation. The experimental results show that this method provides more accurate, efficient, and fast convergence with better stability when approximating the solution of PDEs.

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Section: Wavelets and Cnnmentioning

confidence: 99%

Approximating Partial Differential Equations with Physics-Informed Legendre Multiwavelets CNN

Wang,

et al. 2024

Fractal Fract

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“…Only through the solar panel can we convert the solar energy that we can't use into the power we need. The material of solar panels is semiconductor, mainly crystalline silicon [17][18][19][20]. These crystalline silicon have photosensitive properties.…”

Section: Structure and Working Principle Of Photovoltaic Cellsmentioning

confidence: 99%

Solar Maximum Power Point Tracking Algorithm Based on Wavelet Neural Network

2023

J. Appl. Data Sci.

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With the development of human civilization, the shortage of resources and environmental pollution are increasing. Renewable energy is the only way to solve the problem of harmonious coexistence between human civilization and the environment. More and more of them have come into our lives to reduce the burden of the earth and benefit mankind. Nowadays, due to the increasing gap of traditional power supply, solar energy has become a mainstream renewable energy, with more and more applications, to provide us with green energy and improve our lives. The research on the application of solar energy systems is of great academic value. This paper mainly studies the solar maximum power point tracking (MPPT) algorithm based on wavelet neural network (WNN). This paper analyzes several common maximum power tracking control methods, describes the structure design of WNN maximum power tracking control algorithm, and describes the structure and working principle of photovoltaic cells. In this paper, the output power of MPPT mode is analyzed and compared by simulating the use of solar photovoltaic systems. In the meantime, the output voltage of the solar charging panel in the charging process is studied. The experimental results show that the output power of the power supply in MPPT mode is kept at 0.2, and the output power of the solar panel is improved at every moment with the change of the external environment. At 9 o'clock, the output voltage of the solar panel is 3.6, and at 11 o'clock, the output voltage is 4.11.

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“…The method can accurately handle various types of numerical boundary conditions by effectively managing the fluxes between control volumes. Furthermore, Li et al [31] proposed the DWNN, which combines wavelet transform with neural networks. The method utilized wavelets to obtain a detailed description of the features, which improves the prediction accuracy of the equations.…”

Section: Introductionmentioning

confidence: 99%

RBF-Assisted Hybrid Neural Network for Solving Partial Differential Equations

Li,

Gao,

Ying

2024

Mathematics

Self Cite

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In scientific computing, neural networks have been widely used to solve partial differential equations (PDEs). In this paper, we propose a novel RBF-assisted hybrid neural network for approximating solutions to PDEs. Inspired by the tendency of physics-informed neural networks (PINNs) to become local approximations after training, the proposed method utilizes a radial basis function (RBF) to provide the normalization and localization properties to the input data. The objective of this strategy is to assist the network in solving PDEs more effectively. During the RBF-assisted processing part, the method selects the center points and collocation points separately to effectively manage data size and computational complexity. Subsequently, the RBF processed data are put into the network for predicting the solutions to PDEs. Finally, a series of experiments are conducted to evaluate the novel method. The numerical results confirm that the proposed method can accelerate the convergence speed of the loss function and improve predictive accuracy.

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DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations

Cited by 11 publications

References 57 publications

Approximating Partial Differential Equations with Physics-Informed Legendre Multiwavelets CNN

Approximating Partial Differential Equations with Physics-Informed Legendre Multiwavelets CNN

Solar Maximum Power Point Tracking Algorithm Based on Wavelet Neural Network

RBF-Assisted Hybrid Neural Network for Solving Partial Differential Equations

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