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
The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale dataset...The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.展开更多
Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery...Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse probl...An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.展开更多
The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock captu...The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock capturing methods. The direct problem and the mixed direct-inverse prob- lem of the rotational flow in a transonic plane cascade at both design and off design conditions are solved, and the results show that the present method has rapid convergence rate and high accuracy even for the flow with moderately strong shocks. The calculations have been carried out on the DPS-8 computer, and for the direct problem, only 50-80 iterations are needed, and 50-80 seconds of CPU time are required.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
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.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
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
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
The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (...The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.展开更多
To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy curre...To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.展开更多
In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current ...In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.展开更多
This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-conn...This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.展开更多
Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different ...Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass （3 kD,10 kD,40 kD,70 kD,2 000 kD） were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.展开更多
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partly supported by Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City(2021JJLH0052)National Natural Science Foundation of China(42274154,42304116)+2 种基金Natural Science Foundation of Heilongjiang Province,China(LH2024D013)Heilongjiang Postdoctoral Fund(LBHZ23103)Hainan Yazhou Bay Science and Technology City Jingying Talent Project(SKJC-JYRC-2024-05)。
文摘The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金The project supported by the National Natural Science Foundation of China(10272011)
文摘An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.
文摘The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock capturing methods. The direct problem and the mixed direct-inverse prob- lem of the rotational flow in a transonic plane cascade at both design and off design conditions are solved, and the results show that the present method has rapid convergence rate and high accuracy even for the flow with moderately strong shocks. The calculations have been carried out on the DPS-8 computer, and for the direct problem, only 50-80 iterations are needed, and 50-80 seconds of CPU time are required.
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On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
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.
文摘The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.
基金supported by the National Defense Basic Technology Research Program of China(Grant No.Z132013T001)
文摘To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.
基金Supported by the National Natural Science Foundation of China(11971433)First Class Discipline of Zhe-jiang-A(Zhejiang Gongshang University-Statistics,1020JYN4120004G-091),Graduate Scientic Research and Innovation Foundation of Zhejiang Gongshang University.
文摘In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.
文摘This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.
基金supported by a grant from the National Natural Science Foundation of China (NSFC) No. 81070826/30872886/30400497Sponsored by Shanghai Rising-Star Program No. 09QA1403700+1 种基金funded by Shanghai Leading Academic Discipline Project (Project Number: S30206)the Science and Technology Commission of Shanghai (08DZ2271100)
文摘Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass （3 kD,10 kD,40 kD,70 kD,2 000 kD） were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.
