The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computatio...The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computational fluid dynamics and the flexible rod dynamics is proposed using a two-way domain expansion method.The gov-erning equations of the flexible rod dynamics are discretized and solved by the finite element method,and the fluid flow is simulated by the finite volume method.The interaction between fluids and solid rods is modeled by introducing body force terms into the momentum equations.Referred to the traditional semi-resolved numerical model,an anisotropic Gaussian kernel function method is proposed to specify the interactive forces between flu-ids and solid bodies for non-circle rod cross-sections.A benchmark of the flow passing around a single flexible plate with a rectangular cross-section is used to validate the algorithm.Focused on the engineering applications,a test case of a finite patch of cylinders is implemented to validate the accuracy and efficiency of the coupled model.展开更多
Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the g...Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.展开更多
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ...In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.展开更多
Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep lea...Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.展开更多
The state of health SoH of lithium ion batteries plays a predominant role in ensuring the safe and reliable operation of electric vehicles.In this,a novel SoH estimation approach using support vector regression with a...The state of health SoH of lithium ion batteries plays a predominant role in ensuring the safe and reliable operation of electric vehicles.In this,a novel SoH estimation approach using support vector regression with a Gaussian kernel optimized using the Bayesian optimization technique(BO-SVR with a Gaussian kernel)was proposed.Unlike,traditional approaches that use the internal resistance,and battery capacity as input parameters,this study utilized the equivalent discharging voltage difference interval and equivalent charging voltage difference interval,as they capture the dynamic voltage characteristics associated with the battery degradation.The model was simulated using MATLAB 2023a.The mean absolute error,R^(2),root mean squared error,and mean squared error were considered as performance indicators.The simulation results indicated that the proposed BO-SVR with a Gaussian kernel model had superior performance to other kernel SVR and Gaussian Process Regression models,with a reduced RMSE of 0.0082,thus demonstrating its potential to predict the SoH more accurately.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identifica...A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.展开更多
Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a...Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a curse of dimensionality and thus lead to reduce prediction accuracy.Then the generalization ability of the model will also decline sharply when there are only small samples.To reduce the dimension of calculation and balance the model’s generalization and learning ability,this study proposed a landslide prediction method based on improved principal component analysis(PCA)and mixed kernel function least squares support vector regression(LSSVR)model.First,the traditional PCA was introduced with the idea of linear discrimination,and the dimensions of initial influencing factors were reduced from 8 to 3.The improved PCA can not only weight variables but also extract the original feature.Furthermore,combined with global and local kernel function,the mixed kernel function LSSVR model was framed to improve the generalization ability.Whale optimization algorithm(WOA)was used to optimize the parameters.Moreover,Root Mean Square Error(RMSE),the sum of squared errors(SSE),Mean Absolute Error(MAE),Mean Absolute Precentage Error(MAPE),and reliability were employed to verify the performance of the model.Compared with radial basis function(RBF)LSSVR model,Elman neural network model,and fuzzy decision model,the proposed method has a smaller deviation.Finally,the landslide warning level obtained from the landslide probability can also provide references for relevant decision-making departments in emergency response.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr...In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.展开更多
This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need muc...This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.展开更多
In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth term.The kernel function is used both for determini...In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth term.The kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the algorithm.By developing a new norm-based proximity measure and some technical results,we derive the iteration bound that coincides with the currently best known iteration bound for the algorithm with small-update method.In our knowledge,this result is the first instance of full-Newton step feasible interior-point method for SDO which involving the kernel function.展开更多
A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations o...A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.展开更多
A fast algorithm based on the grayscale distribution of infrared target and the weighted kernel function was proposed for the moving target detection(MTD) in dynamic scene of image series. This algorithm is used to de...A fast algorithm based on the grayscale distribution of infrared target and the weighted kernel function was proposed for the moving target detection(MTD) in dynamic scene of image series. This algorithm is used to deal with issues like the large computational complexity, the fluctuation of grayscale, and the noise in infrared images. Four characteristic points were selected by analyzing the grayscale distribution in infrared image, of which the series was quickly matched with an affine transformation model. The image was then divided into 32×32 squares and the gray-weighted kernel(GWK) for each square was calculated. At last, the MTD was carried out according to the variation of the four GWKs. The results indicate that the MTD can be achieved in real time using the algorithm with the fluctuations of grayscale and noise can be effectively suppressed. The detection probability is greater than 90% with the false alarm rate lower than 5% when the calculation time is less than 40 ms.展开更多
In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bia...In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.展开更多
Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the opti...Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the optimal classified model to extract PPI, this paper presents a strategy to find the optimal kernel function from a kernel function set. The strategy is that in the kernel function set which consists of different single kernel functions, endlessly finding the last two kernel functions on the performance in PPI extraction, using their optimal kernel function to replace them, until there is only one kernel function and it’s the final optimal kernel function. Finally, extracting PPI using the classified model made by this kernel function. This paper conducted the PPI extraction experiment on AIMed corpus, the experimental result shows that the optimal convex combination kernel function this paper presents can effectively improve the extraction performance than single kernel function, and it gets the best precision which reaches 65.0 among the similar PPI extraction systems.展开更多
With the explosive growth of computational resources and data generation,deep machine learning has been successfully employed in various applications.One important and emerging scientific application of deep learning ...With the explosive growth of computational resources and data generation,deep machine learning has been successfully employed in various applications.One important and emerging scientific application of deep learning involves solving differential equations.Here,physics-informed neural networks(PINNs)are developed to solve the differential equations associated with a specific scientific problem.As such,algorithms for solving the differential equations by embedding their initial and boundary conditions in the cost function of the artificial neural networks using algorithmic differentiation must also be developed.In this study,various PINNs are adopted to estimate the stresses in the tablets and the interphase of a single lap joint.The proposed model is represented by two fourth-order non-homogeneous coupled partial differential equations,with the axial stresses in the upper and lower tablets adopted as the dependent variables.The axial stresses are a function of the tablet length,which presents the independent variable.Therefore,the axial stresses in the tablets are estimated by solving the coupled partial differential equations when subjected to the boundary conditions,whereas the remaining stress components are expressed in terms of axial stresses.The results obtained using the developed methodology are validated using the results obtained via MAPLE software.展开更多
Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain anal...Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.展开更多
This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the fea...This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.展开更多
基金supported by Shanghai 2021“Science and Technology Innovation Action Plan”:Social Development Science and Technology Research Project(Grant No.21DZ1202703).
文摘The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computational fluid dynamics and the flexible rod dynamics is proposed using a two-way domain expansion method.The gov-erning equations of the flexible rod dynamics are discretized and solved by the finite element method,and the fluid flow is simulated by the finite volume method.The interaction between fluids and solid rods is modeled by introducing body force terms into the momentum equations.Referred to the traditional semi-resolved numerical model,an anisotropic Gaussian kernel function method is proposed to specify the interactive forces between flu-ids and solid bodies for non-circle rod cross-sections.A benchmark of the flow passing around a single flexible plate with a rectangular cross-section is used to validate the algorithm.Focused on the engineering applications,a test case of a finite patch of cylinders is implemented to validate the accuracy and efficiency of the coupled model.
基金funded by the National Natural Science Foundation of China(General Program:No.52074314,No.U19B6003-05)National Key Research and Development Program of China(2019YFA0708303-05)。
文摘Accurate prediction of formation pore pressure is essential to predict fluid flow and manage hydrocarbon production in petroleum engineering.Recent deep learning technique has been receiving more interest due to the great potential to deal with pore pressure prediction.However,most of the traditional deep learning models are less efficient to address generalization problems.To fill this technical gap,in this work,we developed a new adaptive physics-informed deep learning model with high generalization capability to predict pore pressure values directly from seismic data.Specifically,the new model,named CGP-NN,consists of a novel parametric features extraction approach(1DCPP),a stacked multilayer gated recurrent model(multilayer GRU),and an adaptive physics-informed loss function.Through machine training,the developed model can automatically select the optimal physical model to constrain the results for each pore pressure prediction.The CGP-NN model has the best generalization when the physicsrelated metricλ=0.5.A hybrid approach combining Eaton and Bowers methods is also proposed to build machine-learnable labels for solving the problem of few labels.To validate the developed model and methodology,a case study on a complex reservoir in Tarim Basin was further performed to demonstrate the high accuracy on the pore pressure prediction of new wells along with the strong generalization ability.The adaptive physics-informed deep learning approach presented here has potential application in the prediction of pore pressures coupled with multiple genesis mechanisms using seismic data.
基金Supported by University Science Research Project of Anhui Province(2023AH052921)Outstanding Youth Talent Project of Anhui Province(gxyq2021254)。
文摘In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094).
文摘Efficiently solving partial differential equations(PDEs)is a long-standing challenge in mathematics and physics research.In recent years,the rapid development of artificial intelligence technology has brought deep learning-based methods to the forefront of research on numerical methods for partial differential equations.Among them,physics-informed neural networks(PINNs)are a new class of deep learning methods that show great potential in solving PDEs and predicting complex physical phenomena.In the field of nonlinear science,solitary waves and rogue waves have been important research topics.In this paper,we propose an improved PINN that enhances the physical constraints of the neural network model by adding gradient information constraints.In addition,we employ meta-learning optimization to speed up the training process.We apply the improved PINNs to the numerical simulation and prediction of solitary and rogue waves.We evaluate the accuracy of the prediction results by error analysis.The experimental results show that the improved PINNs can make more accurate predictions in less time than that of the original PINNs.
基金supported by the Royal Academy of Engineering,UK,under the scheme of Distinguished International Associates(DIA-2424-5-134).
文摘The state of health SoH of lithium ion batteries plays a predominant role in ensuring the safe and reliable operation of electric vehicles.In this,a novel SoH estimation approach using support vector regression with a Gaussian kernel optimized using the Bayesian optimization technique(BO-SVR with a Gaussian kernel)was proposed.Unlike,traditional approaches that use the internal resistance,and battery capacity as input parameters,this study utilized the equivalent discharging voltage difference interval and equivalent charging voltage difference interval,as they capture the dynamic voltage characteristics associated with the battery degradation.The model was simulated using MATLAB 2023a.The mean absolute error,R^(2),root mean squared error,and mean squared error were considered as performance indicators.The simulation results indicated that the proposed BO-SVR with a Gaussian kernel model had superior performance to other kernel SVR and Gaussian Process Regression models,with a reduced RMSE of 0.0082,thus demonstrating its potential to predict the SoH more accurately.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
基金Support by China 973 Project (No. 2002CB312200).
文摘A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
基金supported by the Natural Science Foundation of Shaanxi Province(Grant No.2019JQ206)in part by the Science and Technology Department of Shaanxi Province(Grant No.2020CGXNG-009)in part by the Education Department of Shaanxi Province under Grant 17JK0346.
文摘Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a curse of dimensionality and thus lead to reduce prediction accuracy.Then the generalization ability of the model will also decline sharply when there are only small samples.To reduce the dimension of calculation and balance the model’s generalization and learning ability,this study proposed a landslide prediction method based on improved principal component analysis(PCA)and mixed kernel function least squares support vector regression(LSSVR)model.First,the traditional PCA was introduced with the idea of linear discrimination,and the dimensions of initial influencing factors were reduced from 8 to 3.The improved PCA can not only weight variables but also extract the original feature.Furthermore,combined with global and local kernel function,the mixed kernel function LSSVR model was framed to improve the generalization ability.Whale optimization algorithm(WOA)was used to optimize the parameters.Moreover,Root Mean Square Error(RMSE),the sum of squared errors(SSE),Mean Absolute Error(MAE),Mean Absolute Precentage Error(MAPE),and reliability were employed to verify the performance of the model.Compared with radial basis function(RBF)LSSVR model,Elman neural network model,and fuzzy decision model,the proposed method has a smaller deviation.Finally,the landslide warning level obtained from the landslide probability can also provide references for relevant decision-making departments in emergency response.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
基金Supported by the Natural Science Foundation of Hubei Province (2008CDZD47)
文摘In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions.
文摘This paper proposes a physics-informed neural network(PINN)framework to analyze the nonlinear buckling behavior of a three-dimensional(3D)FG porous,slender beam resting on a Winkler-Pasternak foundation.PINNs need much less training data to obtain high accuracy using a straightforward network.The powerful tool used in this work can handle any class of PDEs.We use the deep learning platform TensorFlow and DeepXDE library to design our network.In this study,the PINNs framework takes information from the governing differential equations of the beam system and the data from boundary conditions and outputs the critical nonlinear buckling load.The mathematical model is developed using Hamilton’s principle,considering geometry’s nonlinearity.The accuracy of the modeling framework is carefully examined by applying it to various boundary condition cases as well as the physical parameters such as 3D FG indexes on the nonlinear mechanical behaviors.Finally,the PINNs results are validated with those extracted from the generalized differential quadrature method(GDQM).It is found that the proposed PINN framework can characterize the nonlinear buckling behavior of 3D FG porous,slender beams with satisfactory accuracy.Furthermore,PINN is presented to accurately predict the nonlinear buckling behavior of the beam up to 71 times faster than the numerical method.
基金Supported by University Science Research Project of Anhui Province(KJ2019A1297)University Teaching Research Project of Anhui Province(2019jxtd144)。
文摘In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth term.The kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the algorithm.By developing a new norm-based proximity measure and some technical results,we derive the iteration bound that coincides with the currently best known iteration bound for the algorithm with small-update method.In our knowledge,this result is the first instance of full-Newton step feasible interior-point method for SDO which involving the kernel function.
基金Zhou's research was partially supported by the NNSF of China (10471140, 10571169)Wu's research was partially supported by NNSF of China (0571170)
文摘A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.
基金Project(61101185)supported by the National Natural Science Foundation of China
文摘A fast algorithm based on the grayscale distribution of infrared target and the weighted kernel function was proposed for the moving target detection(MTD) in dynamic scene of image series. This algorithm is used to deal with issues like the large computational complexity, the fluctuation of grayscale, and the noise in infrared images. Four characteristic points were selected by analyzing the grayscale distribution in infrared image, of which the series was quickly matched with an affine transformation model. The image was then divided into 32×32 squares and the gray-weighted kernel(GWK) for each square was calculated. At last, the MTD was carried out according to the variation of the four GWKs. The results indicate that the MTD can be achieved in real time using the algorithm with the fluctuations of grayscale and noise can be effectively suppressed. The detection probability is greater than 90% with the false alarm rate lower than 5% when the calculation time is less than 40 ms.
文摘In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.
文摘Owing to the effect of classified models was different in Protein-Protein Interaction(PPI) extraction, which was made by different single kernel functions, and only using single kernel function hardly trained the optimal classified model to extract PPI, this paper presents a strategy to find the optimal kernel function from a kernel function set. The strategy is that in the kernel function set which consists of different single kernel functions, endlessly finding the last two kernel functions on the performance in PPI extraction, using their optimal kernel function to replace them, until there is only one kernel function and it’s the final optimal kernel function. Finally, extracting PPI using the classified model made by this kernel function. This paper conducted the PPI extraction experiment on AIMed corpus, the experimental result shows that the optimal convex combination kernel function this paper presents can effectively improve the extraction performance than single kernel function, and it gets the best precision which reaches 65.0 among the similar PPI extraction systems.
基金Project supported by the Science and Engineering Research Board(SERB),Department of Science and Technology(DST),India(No.SRG/2019/001581)。
文摘With the explosive growth of computational resources and data generation,deep machine learning has been successfully employed in various applications.One important and emerging scientific application of deep learning involves solving differential equations.Here,physics-informed neural networks(PINNs)are developed to solve the differential equations associated with a specific scientific problem.As such,algorithms for solving the differential equations by embedding their initial and boundary conditions in the cost function of the artificial neural networks using algorithmic differentiation must also be developed.In this study,various PINNs are adopted to estimate the stresses in the tablets and the interphase of a single lap joint.The proposed model is represented by two fourth-order non-homogeneous coupled partial differential equations,with the axial stresses in the upper and lower tablets adopted as the dependent variables.The axial stresses are a function of the tablet length,which presents the independent variable.Therefore,the axial stresses in the tablets are estimated by solving the coupled partial differential equations when subjected to the boundary conditions,whereas the remaining stress components are expressed in terms of axial stresses.The results obtained using the developed methodology are validated using the results obtained via MAPLE software.
文摘Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)Scientific Research Project of Hezhou University(Grant Nos.2014YBZK06 and 2016HZXYSX03)
文摘This paper proposes a new full Nesterov-Todd(NT) step infeasible interior-point algorithm for semidefinite programming. Our algorithm uses a specific kernel function, which is adopted by Liu and Sun, to deduce the feasibility step. By using the step, it is remarkable that in each iteration of the algorithm it needs only one full-NT step, and can obtain an iterate approximate to the central path. Moreover, it is proved that the iterative bound corresponds with the known optimal one for semidefinite optimization problems.
