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Physical informed memory networks for solving PDEs:implementation and applications

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Communications in Theoretical Physics 2024年第2期76卷 51-61页

作者： Jiuyun Sun huanhe dong Yong Fang College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

With the advent of physics informed neural networks(PINNs),deep learning has gained interest for solving nonlinear partial differential equations(PDEs)in recent *** this paper,physics informed memory networks(PIMNs)are proposed as a new approach to solving PDEs by using physical laws and dynamic behavior of *** the fully connected structure of the PINNs,the PIMNs construct the long-term dependence of the dynamics behavior with the help of the long short-term memory ***,the PDEs residuals are approximated using difference schemes in the form of convolution filter,which avoids information loss at the neighborhood of the sampling ***,the performance of the PIMNs is assessed by solving the Kd V equation and the nonlinear Schr?dinger equation,and the effects of difference schemes,boundary conditions,network structure and mesh size on the solutions are *** show that the PIMNs are insensitive to boundary conditions and have excellent solution accuracy even with only the initial conditions.

关键词： nonlinear partial differential equations physics informed memory networks physics informed neural networks numerical solution

Equilibria and Stability Analysis of Cohen-Grossberg BAM Neural Networks on Time Scale

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Journal of Systems Science & Complexity 2022年第4期35卷 1348-1373页

作者： LIU Mingshuo FANG Yong dong huanhe College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

This paper considers the Cohen-Grossberg BAM neural networks(CG-BAMNNs) on time scale, which can unify and generalize the continuous and discrete systems. First, the criteria for the existence and uniqueness of the equilibrium of CG-BAMNNs are derived on time scale. Then based on that, the authors give the criteria for the stability and estimation of equilibrium of the CG-BAMNNs on time scale. The method proposed in this paper unifies and generalizes the continuous and discrete CGBAMNNs systems, and is applicable to some other neural network systems on time scale with practical meaning. The effectiveness of the proposed criteria for delayed CG-BAMNNs is demonstrated by numerical simulation.

关键词： Cohen-Grossberg BAM neural networks existence numerical simulation stability uniqueness

Soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method

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Communications in Theoretical Physics 2022年第7期74卷 30-40页

作者： Yong Zhang Yanwei Ren huanhe dong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China College of Economics and Management Shandong University of Science and TechnologyQingdao 266590China

In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero ***, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time t is large, then we give the comparison between the exact solution and the asymptotic solution.

关键词： robust inverse scattering method modified Korteweg-de Vries equation soliton solution rational travelling waves asymptotic analysis

Time-fractional Davey–Stewartson equation:Lie point symmetries,similarity reductions,conservation laws and traveling wave solutions

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Communications in Theoretical Physics 2023年第10期75卷 10-25页

作者： Baoyong Guo Yong Fang huanhe dong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical *** the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this *** application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are *** the same time,the similarity reductions are ***,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional *** virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential *** using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are ***,the traveling wave solutions are achieved and plotted.

关键词： time-fractional Davey–Stewartson equation Lie symmetry analysis approach Lie point symmetries similarity reductions conservation laws

A(2+1)-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2007年第2期16卷 147-154页

作者： huanhe dong School of Information Shandong University of Science and Technology Qingdao Shandong 266510 China

Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.

关键词： (2+1)维扩散长波分层可积耦合圈代数 (2+1)维零曲率方程

(2+1)-DIMENSIONAL Tu HIERARCHY AND ITS INTEGRABLE COUPLINGS AS WELL AS THE MULTI-COMPONENT INTEGRABLE HIERARCHY

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Annals of Differential Equations 2007年第2期23卷 165-172页

作者： Li Zhu dong huanhe College of Information Science and Engineering Shandong University ofScience and Technology Qingdao 266510 Shandong College of Math. and Information Science Xinyang Normal UniversityXinyang 266510 Henan

Under the frame of the （2＋1）-dimensional zero curvature equation and Tu model, （2＋1）-dimensional Tu hierarchy is obtained. Again by employing a subalgebra of the loop algebra ↑-A2 the integrable coupling system of the above hierarchy is presented. Finally, A multi-component integrable hierarchy is obtained by employing a multi-component loop algebra ↑-GM.

关键词： (2+1)-dimensional zero curvature equation loop algebra multicomponent integrable hierarchy system

THE HAMILTONIAN STRUCTURE OF TWO INTEGRABLE EXPANDING MODELS

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Journal of Partial Differential Equations 2007年第4期20卷 337-348页

作者： Liu Bin dong huanhe Li Zhu Information School Shandong University of Science and Technology Qingdao 266510 China

In this paper, an extended loop algebra is constructed from which an isospectral problem established. It follows that the integrable couplings of the Tu hierarchy and M-AKNS-KN hierarchy are obtained, and their Hamilton structures are presented by the quadratic-form identity. Moreover, we guarantee that the expanding model we obtained are also Liouville integrable.

关键词：哈密尔敦结构可积耦合恒等式自环代数

The Rational Solutions and the Interactions of the N-Soliton Solutions for Boiti-Leon-Manna-Pempinelli-Like Equation

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Journal of Applied Mathematics and Physics 2017年第3期5卷 700-714页

作者： Xiuxiu Liu huanhe dong Yong Zhang Xin Chen Department of Mathematics and Systems Science Shandong University of Science and Technology Qingdao China

These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper, the generalized bilinear method instead of the Hirota bilinear method is used to obtain the rational solutions to the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli-like equation (hereinafter referred to as BLMP equation). Meanwhile, the (2 + 1)-dimensional BLMP-like equation is derived on the basis of the generalized bilinear operators D3,x D3,y and D3,t. And the rational solutions to the (2 + 1)-dimensional BLMP-like equation are obtained successively. Finally, with the help of the N-soliton solutions of the (2 + 1)-dimensional BLMP equation, the interactions of the N-soliton solutions can be derived. The results show that the two soliton still maintained the original waveform after happened collision.

关键词： Rational Solution Generalized Bilinear Method BLMP-Like Equation N-Soliton Solution

Resonance mechanism of flapping wing based on fluid structure interaction simulation

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Chinese Journal of Aeronautics 2024年第5期37卷 243-262页

作者： Yueyang GUO Wenqing YANG Yuanbo dong dong XUE National Key Laboratory of Science and Technology on Aerodynamic Design and Research School of AeronauticsNorthwestern Polytechnical UniversityXi'an 710072China Research&Development Institute of Northwestern Polytechnical University in Shenzhen Shenzhen 518063China Yangtze River Delta Research Institute of Northwestern Polytechnical University Taicang 215400China

Certain insect species have been observed to exploit the resonance mechanism of their *** order to achieve resonance and optimize aerodynamic performance,the conventional approach is to set the flapping frequency of flexible wings based on the Traditional Structural Modal(TSM)***,there exists controversy among researchers regarding the relationship between frequency and aerodynamic *** that the structural response of wings can be influenced by the surrounding air vibrations,an analysis known as Acoustic Structure Interaction Modal(ASIM)is introduced to calculate the resonant *** this study,Fluid Structure Interaction(FSI)simulations are employed to investigate the aerodynamic performance of flapping wings at modal frequencies derived from both TSM and ASIM *** performance is evaluated for various mass ratios and frequency ratios,and the findings indicate that the deformation and changes in vortex structure exhibit similarities at mass ratios that yield the highest aerodynamic ***,the flapping frequency associated with the maximum time-averaged vertical force coefficient at each mass ratio closely aligns with the ASIM frequency,as does the frequency corresponding to maximum ***,the ASIM analysis can provide an effective means for predicting the optimal flapping frequency for flexible ***,it enables the prediction that flexible wings with varying mass ratios will exhibit similar deformation and vortex structure *** paper offers a fresh perspective on the ongoing debate concerning the resonance mechanism of Flexible Flapping Wings(FFWs)and proposes an effective methodology for predicting their aerodynamic performance.

关键词： Flexible Flapping Wing(FFW) Acoustic Structure Interaction Modal(ASIM) Fluid Structure Interaction(FSI) Resonance mechanism Aerodynamic performance