This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new...This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new operator for the structure of the equation in order to apply fixed point theorems. Existence, uniqueness and stability of continuously differentiable solutions are given.展开更多
Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpans...Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.展开更多
Learning to optimize(L2O)stands at the intersection of traditional optimization and machine learning,utilizing the capabilities of machine learning to enhance conventional optimization techniques.As real-world optimiz...Learning to optimize(L2O)stands at the intersection of traditional optimization and machine learning,utilizing the capabilities of machine learning to enhance conventional optimization techniques.As real-world optimization problems frequently share common structures,L2O provides a tool to exploit these structures for better or faster solutions.This tutorial dives deep into L2O techniques,introducing how to accelerate optimization algorithms,promptly estimate the solutions,or even reshape the optimization problem itself,making it more adaptive to real-world applications.By considering the prerequisites for successful applications of L2O and the structure of the optimization problems at hand,this tutorial provides a comprehensive guide for practitioners and researchers alike.展开更多
Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are ...Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.展开更多
The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of in...The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of integration of that function can minimize the worst possible error if the values of the function and its derivative at certain nodes are known.The best interpolation formula used to get the quadrature formula above is also found.Moreover,we compare the best quadrature formula with the open compound corrected trapezoidal formula by theoretical analysis and stochastic experiments.展开更多
Semantic segmentation of driving scene images is crucial for autonomous driving.While deep learning technology has significantly improved daytime image semantic segmentation,nighttime images pose challenges due to fac...Semantic segmentation of driving scene images is crucial for autonomous driving.While deep learning technology has significantly improved daytime image semantic segmentation,nighttime images pose challenges due to factors like poor lighting and overexposure,making it difficult to recognize small objects.To address this,we propose an Image Adaptive Enhancement(IAEN)module comprising a parameter predictor(Edip),multiple image processing filters(Mdif),and a Detail Processing Module(DPM).Edip combines image processing filters to predict parameters like exposure and hue,optimizing image quality.We adopt a novel image encoder to enhance parameter prediction accuracy by enabling Edip to handle features at different scales.DPM strengthens overlooked image details,extending the IAEN module’s functionality.After the segmentation network,we integrate a Depth Guided Filter(DGF)to refine segmentation outputs.The entire network is trained end-to-end,with segmentation results guiding parameter prediction optimization,promoting self-learning and network improvement.This lightweight and efficient network architecture is particularly suitable for addressing challenges in nighttime image segmentation.Extensive experiments validate significant performance improvements of our approach on the ACDC-night and Nightcity datasets.展开更多
In VTI media,the conventional inversion methods based on the existing approximation formulas are difficult to accurately estimate the anisotropic parameters of reservoirs,even more so for unconventional reservoirs wit...In VTI media,the conventional inversion methods based on the existing approximation formulas are difficult to accurately estimate the anisotropic parameters of reservoirs,even more so for unconventional reservoirs with strong seismic anisotropy.Theoretically,the above problems can be solved by utilizing the exact reflection coefficients equations.However,their complicated expression increases the difficulty in calculating the Jacobian matrix when applying them to the Bayesian deterministic inversion.Therefore,the new reduced approximation equations starting from the exact equations are derived here by linearizing the slowness expressions.The relatively simple form and satisfactory calculation accuracy make the reduced equations easy to apply for inversion while ensuring the accuracy of the inversion results.In addition,the blockiness constraint,which follows the differentiable Laplace distribution,is added to the prior model to improve contrasts between layers.Then,the concept of GLI and an iterative reweighted least-squares algorithm is combined to solve the objective function.Lastly,we obtain the iterative solution expression of the elastic parameters and anisotropy parameters and achieve nonlinear AVA inversion based on the reduced equations.The test results of synthetic data and field data show that the proposed method can accurately obtain the VTI parameters from prestack AVA seismic data.展开更多
In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search spa...In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.展开更多
This study addresses the problem of global asymptotic stability for uncertain complex cascade systems composed of multiple integrator systems and non-strict feedforward nonlinear systems. To tackle the complexity inhe...This study addresses the problem of global asymptotic stability for uncertain complex cascade systems composed of multiple integrator systems and non-strict feedforward nonlinear systems. To tackle the complexity inherent in such structures, a novel nested saturated control design is proposed that incorporates both constant saturation levels and state-dependent saturation levels. Specifically, a modified differentiable saturation function is proposed to facilitate the saturation reduction analysis of the uncertain complex cascade systems under the presence of mixed saturation levels. In addition, the design of modified differentiable saturation function will help to construct a hierarchical global convergence strategy to improve the robustness of control design scheme. Through calculation of relevant inequalities, time derivative of boundary surface and simple Lyapunov function,saturation reduction analysis and convergence analysis are carried out, and then a set of explicit parameter conditions are provided to ensure global asymptotic stability in the closed-loop systems. Finally, a simplified system of the mechanical model is presented to validate the effectiveness of the proposed method.展开更多
Learning and inferring underlying motion patterns of captured 2D scenes and then re-creating dynamic evolution consistent with the real-world natural phenomena have high appeal for graphics and animation.To bridge the...Learning and inferring underlying motion patterns of captured 2D scenes and then re-creating dynamic evolution consistent with the real-world natural phenomena have high appeal for graphics and animation.To bridge the technical gap between virtual and real environments,we focus on the inverse modeling and reconstruction of visually consistent and property-verifiable oceans,taking advantage of deep learning and differentiable physics to learn geometry and constitute waves in a self-supervised manner.First,we infer hierarchical geometry using two networks,which are optimized via the differentiable renderer.We extract wave components from the sequence of inferred geometry through a network equipped with a differentiable ocean model.Then,ocean dynamics can be evolved using the reconstructed wave components.Through extensive experiments,we verify that our new method yields satisfactory results for both geometry reconstruction and wave estimation.Moreover,the new framework has the inverse modeling potential to facilitate a host of graphics applications,such as the rapid production of physically accurate scene animation and editing guided by real ocean scenes.展开更多
Template matching is a fundamental task in computer vision and has been studied for decades.It plays an essential role in manufacturing industry for estimating the poses of different parts,facilitating downstream task...Template matching is a fundamental task in computer vision and has been studied for decades.It plays an essential role in manufacturing industry for estimating the poses of different parts,facilitating downstream tasks such as robotic grasping.Existing methods fail when the template and source images have different modalities,cluttered backgrounds,or weak textures.They also rarely consider geometric transformations via homographies,which commonly exist even for planar industrial parts.To tackle the challenges,we propose an accurate template matching method based on differentiable coarse-tofine correspondence refinement.We use an edge-aware module to overcome the domain gap between the mask template and the grayscale image,allowing robust matching.An initial warp is estimated using coarse correspondences based on novel structure-aware information provided by transformers.This initial alignment is passed to a refinement network using references and aligned images to obtain sub-pixel level correspondences which are used to give the final geometric transformation.Extensive evaluation shows that our method to be significantly better than state-of-the-art methods and baselines,providing good generalization ability and visually plausible results even on unseen real data.展开更多
This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of c...This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.展开更多
Dear Editor, This letter is concerned with the data-driven fault compensation tracking control for a coupled wastewater treatment process(WWTP)subject to sensor faults. Invariant set theory is introduced to eliminate ...Dear Editor, This letter is concerned with the data-driven fault compensation tracking control for a coupled wastewater treatment process(WWTP)subject to sensor faults. Invariant set theory is introduced to eliminate the completely bounded and differentiable conditions of coupled non-affine dynamics and to explicitly express the control inputs.An adaptive fault compensation mechanism is constructed to accommodate the effects of sensor faults. By employing a cubic absolutevalue Lyapunov criteria。展开更多
A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear a...A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.展开更多
文摘This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new operator for the structure of the equation in order to apply fixed point theorems. Existence, uniqueness and stability of continuously differentiable solutions are given.
基金Supported both by the National Natural Science Foundation(1 980 1 0 2 3 ) and the Teaching and ResearchAward Fund for Outstanding Young Teachers in Higher Education Institutions of MOEP.R.C
文摘Let E be a uniformly convex Banach space which satisfies Opial's condition or has a Frechet differentiable norm,and C be a bounded closed convex subset of E. If T∶C→C is (asymptotically)nonexpansive,then the modified Ishikawa iteration process defined byx n+1 =t nT ns nT nx n+1-s nx n+(1-t n)x n,converges weakly to a fixed point of T ,where {t n} and {s n} are sequences in [0,1] with some restrictions.
文摘Learning to optimize(L2O)stands at the intersection of traditional optimization and machine learning,utilizing the capabilities of machine learning to enhance conventional optimization techniques.As real-world optimization problems frequently share common structures,L2O provides a tool to exploit these structures for better or faster solutions.This tutorial dives deep into L2O techniques,introducing how to accelerate optimization algorithms,promptly estimate the solutions,or even reshape the optimization problem itself,making it more adaptive to real-world applications.By considering the prerequisites for successful applications of L2O and the structure of the optimization problems at hand,this tutorial provides a comprehensive guide for practitioners and researchers alike.
文摘Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.
基金supported by the Special Funds for Major State Basic Research Projects(Grant No.G19990328)the National and Zhejiang Provincial Natural Science Foundation of China(Grant No.10471128 and Grant No.101027).
文摘The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of integration of that function can minimize the worst possible error if the values of the function and its derivative at certain nodes are known.The best interpolation formula used to get the quadrature formula above is also found.Moreover,we compare the best quadrature formula with the open compound corrected trapezoidal formula by theoretical analysis and stochastic experiments.
基金This work is supported in part by The National Natural Science Foundation of China(Grant Number 61971078),which provided domain expertise and computational power that greatly assisted the activityThis work was financially supported by Chongqing Municipal Education Commission Grants for-Major Science and Technology Project(Grant Number gzlcx20243175).
文摘Semantic segmentation of driving scene images is crucial for autonomous driving.While deep learning technology has significantly improved daytime image semantic segmentation,nighttime images pose challenges due to factors like poor lighting and overexposure,making it difficult to recognize small objects.To address this,we propose an Image Adaptive Enhancement(IAEN)module comprising a parameter predictor(Edip),multiple image processing filters(Mdif),and a Detail Processing Module(DPM).Edip combines image processing filters to predict parameters like exposure and hue,optimizing image quality.We adopt a novel image encoder to enhance parameter prediction accuracy by enabling Edip to handle features at different scales.DPM strengthens overlooked image details,extending the IAEN module’s functionality.After the segmentation network,we integrate a Depth Guided Filter(DGF)to refine segmentation outputs.The entire network is trained end-to-end,with segmentation results guiding parameter prediction optimization,promoting self-learning and network improvement.This lightweight and efficient network architecture is particularly suitable for addressing challenges in nighttime image segmentation.Extensive experiments validate significant performance improvements of our approach on the ACDC-night and Nightcity datasets.
文摘In VTI media,the conventional inversion methods based on the existing approximation formulas are difficult to accurately estimate the anisotropic parameters of reservoirs,even more so for unconventional reservoirs with strong seismic anisotropy.Theoretically,the above problems can be solved by utilizing the exact reflection coefficients equations.However,their complicated expression increases the difficulty in calculating the Jacobian matrix when applying them to the Bayesian deterministic inversion.Therefore,the new reduced approximation equations starting from the exact equations are derived here by linearizing the slowness expressions.The relatively simple form and satisfactory calculation accuracy make the reduced equations easy to apply for inversion while ensuring the accuracy of the inversion results.In addition,the blockiness constraint,which follows the differentiable Laplace distribution,is added to the prior model to improve contrasts between layers.Then,the concept of GLI and an iterative reweighted least-squares algorithm is combined to solve the objective function.Lastly,we obtain the iterative solution expression of the elastic parameters and anisotropy parameters and achieve nonlinear AVA inversion based on the reduced equations.The test results of synthetic data and field data show that the proposed method can accurately obtain the VTI parameters from prestack AVA seismic data.
基金This work was supported in part by the National Natural Science Foundation of China under Grant 61305001the Natural Science Foundation of Heilongjiang Province of China under Grant F201222.
文摘In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.
基金supported in part by the National Natural Science Foundation of China (62203178, U1913602, 61936004)the National Key Rsearch and Development Program of China (2021ZD0201300)+3 种基金the China Postdoctoral Science Foundation (2021TQ0116)the Innovation Group Project of the National Natural Science Foundation of China (61821003)the Technology Innovation Project of Hubei Province of China (2019AE A171)the 111 Project on Computational Intelligence and Intelligent Control (B18024)。
文摘This study addresses the problem of global asymptotic stability for uncertain complex cascade systems composed of multiple integrator systems and non-strict feedforward nonlinear systems. To tackle the complexity inherent in such structures, a novel nested saturated control design is proposed that incorporates both constant saturation levels and state-dependent saturation levels. Specifically, a modified differentiable saturation function is proposed to facilitate the saturation reduction analysis of the uncertain complex cascade systems under the presence of mixed saturation levels. In addition, the design of modified differentiable saturation function will help to construct a hierarchical global convergence strategy to improve the robustness of control design scheme. Through calculation of relevant inequalities, time derivative of boundary surface and simple Lyapunov function,saturation reduction analysis and convergence analysis are carried out, and then a set of explicit parameter conditions are provided to ensure global asymptotic stability in the closed-loop systems. Finally, a simplified system of the mechanical model is presented to validate the effectiveness of the proposed method.
基金sponsored by grants from the National Natural Science Foundation of China(62002010,61872347)the CAMS Innovation Fund for Medical Sciences(2019-I2M5-016)the Special Plan for the Development of Distinguished Young Scientists of ISCAS(Y8RC535018).
文摘Learning and inferring underlying motion patterns of captured 2D scenes and then re-creating dynamic evolution consistent with the real-world natural phenomena have high appeal for graphics and animation.To bridge the technical gap between virtual and real environments,we focus on the inverse modeling and reconstruction of visually consistent and property-verifiable oceans,taking advantage of deep learning and differentiable physics to learn geometry and constitute waves in a self-supervised manner.First,we infer hierarchical geometry using two networks,which are optimized via the differentiable renderer.We extract wave components from the sequence of inferred geometry through a network equipped with a differentiable ocean model.Then,ocean dynamics can be evolved using the reconstructed wave components.Through extensive experiments,we verify that our new method yields satisfactory results for both geometry reconstruction and wave estimation.Moreover,the new framework has the inverse modeling potential to facilitate a host of graphics applications,such as the rapid production of physically accurate scene animation and editing guided by real ocean scenes.
基金supported in part by the National Key R&D Program of China(2018AAA0102200)the National Natural Science Foundation of China(62002375,62002376,62325221,62132021).
文摘Template matching is a fundamental task in computer vision and has been studied for decades.It plays an essential role in manufacturing industry for estimating the poses of different parts,facilitating downstream tasks such as robotic grasping.Existing methods fail when the template and source images have different modalities,cluttered backgrounds,or weak textures.They also rarely consider geometric transformations via homographies,which commonly exist even for planar industrial parts.To tackle the challenges,we propose an accurate template matching method based on differentiable coarse-tofine correspondence refinement.We use an edge-aware module to overcome the domain gap between the mask template and the grayscale image,allowing robust matching.An initial warp is estimated using coarse correspondences based on novel structure-aware information provided by transformers.This initial alignment is passed to a refinement network using references and aligned images to obtain sub-pixel level correspondences which are used to give the final geometric transformation.Extensive evaluation shows that our method to be significantly better than state-of-the-art methods and baselines,providing good generalization ability and visually plausible results even on unseen real data.
基金the Natural Science Foundation ofFujian Province of China(S0650021,2006J0215)the National Natural Science Foundation of China(10771086)
文摘This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.
基金supported by the National Natural Science Foundation of China(61890930-3,62173145)National Natural Science Fund for Distinguished Young Scholars(61925305)Shanghai Pujiang Program(21PJ1402200)and Shanghai AI Laboratory。
文摘Dear Editor, This letter is concerned with the data-driven fault compensation tracking control for a coupled wastewater treatment process(WWTP)subject to sensor faults. Invariant set theory is introduced to eliminate the completely bounded and differentiable conditions of coupled non-affine dynamics and to explicitly express the control inputs.An adaptive fault compensation mechanism is constructed to accommodate the effects of sensor faults. By employing a cubic absolutevalue Lyapunov criteria。
文摘A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.
