In this paper,the authors propose Neumann series neural operator(NSNO)to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions.Helmholtz equation is a crucial ...In this paper,the authors propose Neumann series neural operator(NSNO)to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions.Helmholtz equation is a crucial partial differential equation(PDE)with applications in various scientific and engineering fields.However,efficient solver of Helmholtz equation is still a big challenge especially in the case of high wavenumber.Recently,deep learning has shown great potential in solving PDEs especially in learning solution operators.Inspired by Neumann series in Helmholtz equation,the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale feature.Extensive experiments show that the proposed NSNO significantly outperforms the state-of-the-art FNO with at least 60%lower relative L^(2)-error,especially in the large wavenumber case,and has 50%lower computational cost and less data requirement.Moreover,NSNO can be used as the surrogate model in inverse scattering problems.Numerical tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.展开更多
The research purpose of this paper is focused on investigating the performance of extra-large scale massive multiple-input multiple-output(XL-MIMO)systems with residual hardware impairments.The closed-form expression ...The research purpose of this paper is focused on investigating the performance of extra-large scale massive multiple-input multiple-output(XL-MIMO)systems with residual hardware impairments.The closed-form expression of the achievable rate under the match filter(MF)receiving strategy was derived and the influence of spatial non-stationarity and residual hardware impairments on the system performance was investigated.In order to maximize the signal-to-interference-plus-noise ratio(SINR)of the systems in the presence of hardware impairments,a hardware impairments-aware minimum mean squared error(HIA-MMSE)receiver was proposed.Furthermore,the stair Neumann series approximation was used to reduce the computational complexity of the HIA-MMSE receiver,which can avoid matrix inversion.Simulation results demonstrate the tightness of the derived analytical expressions and the effectiveness of the low complexity HIA-MMSE(LC-HIA-MMSE)receiver.展开更多
Based on viscoelastic Kelvin.model and：nonlocal relationship of strain and stress, a nonlocal constitutive relationshila of viscoelasticity is obtained and the strain response of a bar in tension is studied, By trans...Based on viscoelastic Kelvin.model and：nonlocal relationship of strain and stress, a nonlocal constitutive relationshila of viscoelasticity is obtained and the strain response of a bar in tension is studied, By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the closed-form s.olution of strain field of the bar is obtained.： The creep process of the bar is presented： When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity展开更多
基金supported by the National Science Foundation of China under Grant No.92370125the National Key R&D Program of China under Grant Nos.2019YFA0709600 and 2019YFA0709602.
文摘In this paper,the authors propose Neumann series neural operator(NSNO)to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions.Helmholtz equation is a crucial partial differential equation(PDE)with applications in various scientific and engineering fields.However,efficient solver of Helmholtz equation is still a big challenge especially in the case of high wavenumber.Recently,deep learning has shown great potential in solving PDEs especially in learning solution operators.Inspired by Neumann series in Helmholtz equation,the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale feature.Extensive experiments show that the proposed NSNO significantly outperforms the state-of-the-art FNO with at least 60%lower relative L^(2)-error,especially in the large wavenumber case,and has 50%lower computational cost and less data requirement.Moreover,NSNO can be used as the surrogate model in inverse scattering problems.Numerical tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.
基金supported by the National Natural Science Foundation of China(61672484)。
文摘The research purpose of this paper is focused on investigating the performance of extra-large scale massive multiple-input multiple-output(XL-MIMO)systems with residual hardware impairments.The closed-form expression of the achievable rate under the match filter(MF)receiving strategy was derived and the influence of spatial non-stationarity and residual hardware impairments on the system performance was investigated.In order to maximize the signal-to-interference-plus-noise ratio(SINR)of the systems in the presence of hardware impairments,a hardware impairments-aware minimum mean squared error(HIA-MMSE)receiver was proposed.Furthermore,the stair Neumann series approximation was used to reduce the computational complexity of the HIA-MMSE receiver,which can avoid matrix inversion.Simulation results demonstrate the tightness of the derived analytical expressions and the effectiveness of the low complexity HIA-MMSE(LC-HIA-MMSE)receiver.
基金Project supported by the Science Foundation ofNational University of Defense Technology(No.JC0601-01)
文摘Based on viscoelastic Kelvin.model and：nonlocal relationship of strain and stress, a nonlocal constitutive relationshila of viscoelasticity is obtained and the strain response of a bar in tension is studied, By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the closed-form s.olution of strain field of the bar is obtained.： The creep process of the bar is presented： When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity
