The phonon density of states of YBa2Cu3O6.92 is obtained with the method of Fourier decon-volution and Tikhonov-s regularization technique from the experimental specific heat data. The result is compared with that of ...The phonon density of states of YBa2Cu3O6.92 is obtained with the method of Fourier decon-volution and Tikhonov-s regularization technique from the experimental specific heat data. The result is compared with that of neutron inelastic scattering.展开更多
The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method f...The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.展开更多
By using Lax representation, we study the separation of variables for x- and tn-finitedimensional integrable Hamiltonian system (FDIHS) obtained from the factorization of AKNShierarchy. Then the separability of X- and...By using Lax representation, we study the separation of variables for x- and tn-finitedimensional integrable Hamiltonian system (FDIHS) obtained from the factorization of AKNShierarchy. Then the separability of X- and tn-FDIHS and the factorization of AKNS hierarchy give rise to the Jacobi inversion problem for soliton equations in AKNS hierarchy. By a standard Jacobi inversion technique, the soliton equations can be solved in terms of Riemann theta function.展开更多
Solutions of inverse problems are required in various fields of science and engineering. The concept of network inversion has been studied as a neural-network-based solution to inverse problems. In general, inverse pr...Solutions of inverse problems are required in various fields of science and engineering. The concept of network inversion has been studied as a neural-network-based solution to inverse problems. In general, inverse problems are not limited to a real-valued area. Recently, complex-valued neural networks have been actively studied in the field of neural networks. As an extension of network inversion to complex numbers, a complex-valued network inversion has been proposed. Moreover, inverse problems for estimating the parameters of distributed generation systems such as distributed energy plants or smart grids from observed electric circuit data have been studied in the field of natural energy. These emphasize the need to handle complex numbers in an alternating current （AC） circuit. In this paper, the authors propose an application of the complex-valued network inversion to the inverse estimation of a distributed generation. Further, the authors confirm the effectiveness of the complex-valued network inversion on the basis of simulation results.展开更多
Ultrasound computed tomography(USCT)is a noninvasive biomedical imaging modality that offers insights into acoustic properties such as the sound speed(SS)and acoustic attenuation(AA)of the human body,enhancing diagnos...Ultrasound computed tomography(USCT)is a noninvasive biomedical imaging modality that offers insights into acoustic properties such as the sound speed(SS)and acoustic attenuation(AA)of the human body,enhancing diagnostic accuracy and therapy planning.Full waveform inversion(FWI)is a promising USCT image reconstruction method that optimizes the parameter fields of a wave propagation model via gradient-based optimization.However,twodimensional FWI methods are limited by their inability to account for three-dimensional wave propagation in the elevation direction,resulting in image artifacts.To address this problem,we propose a three-dimensional time-domain full waveform inversion algorithm to reconstruct the SS and AA distributions on the basis of a fractional Laplacian wave equation,adjoint field formulation,and gradient descent optimization.Validated by two sets of simulations,the proposed algorithm has potential for generating high-resolution and quantitative SS and AA distributions.This approach holds promise for clinical USCT applications,assisting early disease detection,precise abnormality localization,and optimized treatment planning,thus contributing to better healthcare outcomes.展开更多
In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reve...In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum leng...Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.展开更多
Because of the constraint mode of the inversion objective function in the traditional resistivity-inversion method of electromagnetic-propagation resistivity logging while drilling(EPR-LWD),obvious differences appear ...Because of the constraint mode of the inversion objective function in the traditional resistivity-inversion method of electromagnetic-propagation resistivity logging while drilling(EPR-LWD),obvious differences appear in the radial and vertical investigation characteristics between the amplitude-ratio and phase difference,which affect the practical application of EPR-LWD data.In this paper,according to the EPR-LWD data,a self-adaptive constraint resistivity-inversion method,which adopts a self-adaptive constraint weighted expression in the objective function to balance the contributions of the phase difference and amplitude attenuation,is proposed.A particle swarm optimization algorithm is also introduced to eliminate the dependence of the accuracy and convergence on the initial value of the inversion.According to the inversion results of multiple classical formation models for EPR-LWD,the differences between the adaptive constraint inversion-resistivity logs with the traditional amplitude-ratio and the phase difference of the resistivity logs are discussed in detail.The results demonstrate that the adaptive resistivity logs take into account the advantages of the amplitude-ratio logs in the radial investigation and phase difference logs in the vertical resolution.Further,it is superior in thin-layer identification and invasion-effect appraisal compared with the single-amplitude-ratio and phase difference logs.The inversion results can provide a theoretical reference for research on the resistivity-inversion method of electromagnetic wave LWD.展开更多
A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. Th...A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.展开更多
Optimizing the rotor pole-shoe structure of large salient pole synchronous motors is critical for improving their performance and efficiency,allowing for enhanced responsiveness to grid demands and adjustments in oper...Optimizing the rotor pole-shoe structure of large salient pole synchronous motors is critical for improving their performance and efficiency,allowing for enhanced responsiveness to grid demands and adjustments in operating conditions.This paper provides a comprehensive review of various pole-shoe structures for salient pole synchronous motor rotors and their associated optimization techniques.First,it outlines the role of the pole-shoe structure and examines the theoretical theories of key electromagnetic parameters,including the pole-arc coefficient,voltage waveform coefficient,and armature reaction coefficient.Regarding structural design,this paper explores several configurations,including the threesegment arc,five-segment arc,single eccentric pole-arc combined with two chordal surface sections,and asymmetric poles.The effects of these designs on the air-gap magnetic field distribution and voltage waveform are evaluated.In terms of methodology,this paper reviews the application of numerical solutions to electromagnetic field inverse problems and the use of optimization algorithms for electrical machine structural optimization.This study illustrates the application of improved simulated annealing algorithms,tabu search algorithms,and particle swarm optimization algorithms for single-objective optimization of five-segment arc pole-shoe structures.Additionally,this paper discusses the use of vector tabu search and multi-objective quantum evolutionary algorithms for the multi-objective optimization of five-segment arc pole-shoe structures.The study concludes that multi-objective optimization algorithms are underutilized for pole-shoe structure optimization and suggests that multi-objective particle swarm optimization could be more extensively employed for this purpose.Furthermore,the potential application of topology optimization methods for the design of salient-pole synchronous motor rotor magnetic poles is proposed.展开更多
Small angle x-ray scattering(SAXS)is an advanced technique for characterizing the particle size distribution(PSD)of nanoparticles.However,the ill-posed nature of inverse problems in SAXS data analysis often reduces th...Small angle x-ray scattering(SAXS)is an advanced technique for characterizing the particle size distribution(PSD)of nanoparticles.However,the ill-posed nature of inverse problems in SAXS data analysis often reduces the accuracy of conventional methods.This article proposes a user-friendly software for PSD analysis,GranuSAS,which employs an algorithm that integrates truncated singular value decomposition(TSVD)with the Chahine method.This approach employs TSVD for data preprocessing,generating a set of initial solutions with noise suppression.A high-quality initial solution is subsequently selected via the L-curve method.This selected candidate solution is then iteratively refined by the Chahine algorithm,enforcing constraints such as non-negativity and improving physical interpretability.Most importantly,GranuSAS employs a parallel architecture that simultaneously yields inversion results from multiple shape models and,by evaluating the accuracy of each model's reconstructed scattering curve,offers a suggestion for model selection in material systems.To systematically validate the accuracy and efficiency of the software,verification was performed using both simulated and experimental datasets.The results demonstrate that the proposed software delivers both satisfactory accuracy and reliable computational efficiency.It provides an easy-to-use and reliable tool for researchers in materials science,helping them fully exploit the potential of SAXS in nanoparticle characterization.展开更多
Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performan...Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.展开更多
We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy.In this procedure,a coarse grid of training points is used at the initial training s...We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy.In this procedure,a coarse grid of training points is used at the initial training stages,while more points are added at later stages based on the value of the residual at a larger set of evaluation points.This method increases the robustness of the neural network approximation and can result in significant computational savings,particularly when the solution is non-smooth.Numerical results are presented for benchmark problems for scalar-valued PDEs,namely Poisson and Helmholtz equations,as well as for an inverse acoustics problem.展开更多
Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can ...Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.展开更多
Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the pred...Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.展开更多
Wavelet network, a class of neural network consisting of wavelets, is proposed to solve the inverse kinematics problem in robotic manipulator. A wavelet network suitable for dealing with multi-input and multi-output s...Wavelet network, a class of neural network consisting of wavelets, is proposed to solve the inverse kinematics problem in robotic manipulator. A wavelet network suitable for dealing with multi-input and multi-output system is constructed. The network is optimized by reducing the number of wavelets handling large dimension problem according to the sample data. The algorithms for sparseness analysis of input data and fitting wavelets to the output data with orthogonal method are introduced. Then Levenberg-Marquardt algorithm is used to train the network. Simulation results showed that this method is capable of solving the inverse kinematics problem for PUMA560.展开更多
This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the...This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.展开更多
A novel method based on the relevance vector machine（RVM） for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.T...A novel method based on the relevance vector machine（RVM） for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine（SVM） based approach.展开更多
In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is...In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost func- tional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.展开更多
文摘The phonon density of states of YBa2Cu3O6.92 is obtained with the method of Fourier decon-volution and Tikhonov-s regularization technique from the experimental specific heat data. The result is compared with that of neutron inelastic scattering.
基金Supported by the National Basic Research Project forNonlinear Sciences and the Doctorate DissertationFoundation of Tsinghua University
文摘The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.
文摘By using Lax representation, we study the separation of variables for x- and tn-finitedimensional integrable Hamiltonian system (FDIHS) obtained from the factorization of AKNShierarchy. Then the separability of X- and tn-FDIHS and the factorization of AKNS hierarchy give rise to the Jacobi inversion problem for soliton equations in AKNS hierarchy. By a standard Jacobi inversion technique, the soliton equations can be solved in terms of Riemann theta function.
文摘Solutions of inverse problems are required in various fields of science and engineering. The concept of network inversion has been studied as a neural-network-based solution to inverse problems. In general, inverse problems are not limited to a real-valued area. Recently, complex-valued neural networks have been actively studied in the field of neural networks. As an extension of network inversion to complex numbers, a complex-valued network inversion has been proposed. Moreover, inverse problems for estimating the parameters of distributed generation systems such as distributed energy plants or smart grids from observed electric circuit data have been studied in the field of natural energy. These emphasize the need to handle complex numbers in an alternating current （AC） circuit. In this paper, the authors propose an application of the complex-valued network inversion to the inverse estimation of a distributed generation. Further, the authors confirm the effectiveness of the complex-valued network inversion on the basis of simulation results.
基金supported by the National Key Research and Development Program of China(2022YFA1404400)the National Natural Science Foundation of China(62122072,12174368,61705216,62405306)+4 种基金Anhui Provincial Department of Science and Technology(202203a07020020,18030801138)Anhui Provincial Natural Science Foundation(2308085QA21,2408085QF187)the USTC Research Funds of the Double First-Class Initiative(YD2090002015)the Institute of Artificial Intelligence at Hefei Comprehensive National Science Center(23YGXT005)the Fundamental Research Funds for the Central Universities(WK2090000083).
文摘Ultrasound computed tomography(USCT)is a noninvasive biomedical imaging modality that offers insights into acoustic properties such as the sound speed(SS)and acoustic attenuation(AA)of the human body,enhancing diagnostic accuracy and therapy planning.Full waveform inversion(FWI)is a promising USCT image reconstruction method that optimizes the parameter fields of a wave propagation model via gradient-based optimization.However,twodimensional FWI methods are limited by their inability to account for three-dimensional wave propagation in the elevation direction,resulting in image artifacts.To address this problem,we propose a three-dimensional time-domain full waveform inversion algorithm to reconstruct the SS and AA distributions on the basis of a fractional Laplacian wave equation,adjoint field formulation,and gradient descent optimization.Validated by two sets of simulations,the proposed algorithm has potential for generating high-resolution and quantitative SS and AA distributions.This approach holds promise for clinical USCT applications,assisting early disease detection,precise abnormality localization,and optimized treatment planning,thus contributing to better healthcare outcomes.
文摘In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金supported by the National Natural Science Foundation of China(No.12301425)。
文摘Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.
基金supported by the Foundation of Key Laboratory of Exploration Technology for Oil and Gas Resources of the Ministry of Education, Yangtze University, Wuhan (No. K201812)the Foundation of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing (No. PRP/open-1704)the Foundation of Education of Hubei Province, China (No. Q20171304)。
文摘Because of the constraint mode of the inversion objective function in the traditional resistivity-inversion method of electromagnetic-propagation resistivity logging while drilling(EPR-LWD),obvious differences appear in the radial and vertical investigation characteristics between the amplitude-ratio and phase difference,which affect the practical application of EPR-LWD data.In this paper,according to the EPR-LWD data,a self-adaptive constraint resistivity-inversion method,which adopts a self-adaptive constraint weighted expression in the objective function to balance the contributions of the phase difference and amplitude attenuation,is proposed.A particle swarm optimization algorithm is also introduced to eliminate the dependence of the accuracy and convergence on the initial value of the inversion.According to the inversion results of multiple classical formation models for EPR-LWD,the differences between the adaptive constraint inversion-resistivity logs with the traditional amplitude-ratio and the phase difference of the resistivity logs are discussed in detail.The results demonstrate that the adaptive resistivity logs take into account the advantages of the amplitude-ratio logs in the radial investigation and phase difference logs in the vertical resolution.Further,it is superior in thin-layer identification and invasion-effect appraisal compared with the single-amplitude-ratio and phase difference logs.The inversion results can provide a theoretical reference for research on the resistivity-inversion method of electromagnetic wave LWD.
文摘A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A=｛A∈R n×m ｜‖AX-B‖ F=min｝ is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold.
文摘Optimizing the rotor pole-shoe structure of large salient pole synchronous motors is critical for improving their performance and efficiency,allowing for enhanced responsiveness to grid demands and adjustments in operating conditions.This paper provides a comprehensive review of various pole-shoe structures for salient pole synchronous motor rotors and their associated optimization techniques.First,it outlines the role of the pole-shoe structure and examines the theoretical theories of key electromagnetic parameters,including the pole-arc coefficient,voltage waveform coefficient,and armature reaction coefficient.Regarding structural design,this paper explores several configurations,including the threesegment arc,five-segment arc,single eccentric pole-arc combined with two chordal surface sections,and asymmetric poles.The effects of these designs on the air-gap magnetic field distribution and voltage waveform are evaluated.In terms of methodology,this paper reviews the application of numerical solutions to electromagnetic field inverse problems and the use of optimization algorithms for electrical machine structural optimization.This study illustrates the application of improved simulated annealing algorithms,tabu search algorithms,and particle swarm optimization algorithms for single-objective optimization of five-segment arc pole-shoe structures.Additionally,this paper discusses the use of vector tabu search and multi-objective quantum evolutionary algorithms for the multi-objective optimization of five-segment arc pole-shoe structures.The study concludes that multi-objective optimization algorithms are underutilized for pole-shoe structure optimization and suggests that multi-objective particle swarm optimization could be more extensively employed for this purpose.Furthermore,the potential application of topology optimization methods for the design of salient-pole synchronous motor rotor magnetic poles is proposed.
基金Project supported by the Project of the Anhui Provincial Natural Science Foundation(Grant No.2308085MA19)Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA0410401)+2 种基金the National Natural Science Foundation of China(Grant No.52202120)the National Key Research and Development Program of China(Grant No.2023YFA1609800)USTC Research Funds of the Double First-Class Initiative(Grant No.YD2310002013)。
文摘Small angle x-ray scattering(SAXS)is an advanced technique for characterizing the particle size distribution(PSD)of nanoparticles.However,the ill-posed nature of inverse problems in SAXS data analysis often reduces the accuracy of conventional methods.This article proposes a user-friendly software for PSD analysis,GranuSAS,which employs an algorithm that integrates truncated singular value decomposition(TSVD)with the Chahine method.This approach employs TSVD for data preprocessing,generating a set of initial solutions with noise suppression.A high-quality initial solution is subsequently selected via the L-curve method.This selected candidate solution is then iteratively refined by the Chahine algorithm,enforcing constraints such as non-negativity and improving physical interpretability.Most importantly,GranuSAS employs a parallel architecture that simultaneously yields inversion results from multiple shape models and,by evaluating the accuracy of each model's reconstructed scattering curve,offers a suggestion for model selection in material systems.To systematically validate the accuracy and efficiency of the software,verification was performed using both simulated and experimental datasets.The results demonstrate that the proposed software delivers both satisfactory accuracy and reliable computational efficiency.It provides an easy-to-use and reliable tool for researchers in materials science,helping them fully exploit the potential of SAXS in nanoparticle characterization.
基金Supported by the National Key Research and Development Program of China(No.2023YFC3008200)the Independent Research Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(No.SML2022SP505)。
文摘Physics-informed neural networks(PINNs),as a novel artificial intelligence method for solving partial differential equations,are applicable to solve both forward and inverse problems.This study evaluates the performance of PINNs in solving the temperature diffusion equation of the seawater across six scenarios,including forward and inverse problems under three different boundary conditions.Results demonstrate that PINNs achieved consistently higher accuracy with the Dirichlet and Neumann boundary conditions compared to the Robin boundary condition for both forward and inverse problems.Inaccurate weighting of terms in the loss function can reduce model accuracy.Additionally,the sensitivity of model performance to the positioning of sampling points varied between different boundary conditions.In particular,the model under the Dirichlet boundary condition exhibited superior robustness to variations in point positions during the solutions of inverse problems.In contrast,for the Neumann and Robin boundary conditions,accuracy declines when points were sampled from identical positions or at the same time.Subsequently,the Argo observations were used to reconstruct the vertical diffusion of seawater temperature in the north-central Pacific for the applicability of PINNs in the real ocean.The PINNs successfully captured the vertical diffusion characteristics of seawater temperature,reflected the seasonal changes of vertical temperature under different topographic conditions,and revealed the influence of topography on the temperature diffusion coefficient.The PINNs were proved effective in solving the temperature diffusion equation of seawater with limited data,providing a promising technique for simulating or predicting ocean phenomena using sparse observations.
文摘We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy.In this procedure,a coarse grid of training points is used at the initial training stages,while more points are added at later stages based on the value of the residual at a larger set of evaluation points.This method increases the robustness of the neural network approximation and can result in significant computational savings,particularly when the solution is non-smooth.Numerical results are presented for benchmark problems for scalar-valued PDEs,namely Poisson and Helmholtz equations,as well as for an inverse acoustics problem.
基金Project supported by the Special Scientific Research Project for Public Interest(Grant No.GYHY201206009)the Fundamental Research Funds for the Central Universities,China(Grant Nos.lzujbky-2012-13 and lzujbky-2013-11)the National Basic Research Program of China(Grant Nos.2012CB955902 and 2013CB430204)
文摘Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
文摘Wavelet network, a class of neural network consisting of wavelets, is proposed to solve the inverse kinematics problem in robotic manipulator. A wavelet network suitable for dealing with multi-input and multi-output system is constructed. The network is optimized by reducing the number of wavelets handling large dimension problem according to the sample data. The algorithms for sparseness analysis of input data and fitting wavelets to the output data with orthogonal method are introduced. Then Levenberg-Marquardt algorithm is used to train the network. Simulation results showed that this method is capable of solving the inverse kinematics problem for PUMA560.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10272021, 10572021） and the Doctoral Programme Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61071022)the Graduate Student Research and Innovation Program of Jiangsu Province,China (Grant No. CXZZ11-0381)
文摘A novel method based on the relevance vector machine（RVM） for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine（SVM） based approach.
基金supported in part by the CNRST Morocco,the Volkswagen Foundation:Grant number I/79315Hydromed project
文摘In the present work, we investigate the inverse problem of reconstructing the parameter of an integro-differential parabolic equation, which comes from pollution problems in porous media, when the final observation is given. We use the optimal control framework to establish both the existence and necessary condition of the minimizer for the cost func- tional. Furthermore, we prove the stability and the local uniqueness of the minimizer. Some numerical results will be presented and discussed.
