Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,whic...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
作者：
GUO YixiaoMING PingbingLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architectu...
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The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.
We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic ***,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the ...
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We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic ***,we propose a specific algorithm termed STRME,in which the trust-region radius depends linearly on the gradient used to define the latest *** complexity results of the STRME method in nonconvex,convex and strongly convex settings are presented,which match those of the existing algorithms based on probabilistic *** addition,several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.
作者：
Xiaodong FengLi ZengTao ZhouLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesBeijingChina
In this work,we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck(TFP)*** is well known that solutions of such equations are probability density functio...
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In this work,we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck(TFP)*** is well known that solutions of such equations are probability density functions,and thus our approach relies on modelling the target solutions with the temporal normalizing *** temporal normalizing flow is then trained based on the TFP loss function,without requiring any labeled *** a machine learning scheme,the proposed approach is mesh-free and can be easily applied to high dimensional *** present a variety of test problems to show the effectiveness of the learning approach.
作者：
Xianmin XuLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingNCMISAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow *** show that the discretized problem has the same energy dissipation structure...
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By using the Onsager principle as an approximation tool,we give a novel derivation for the moving finite element method for gradient flow *** show that the discretized problem has the same energy dissipation structure as the continuous *** enables us to do numerical analysis for the stationary solution of a nonlinear reaction diffusion equation using the approximation theory of free-knot piecewise *** show that under certain conditions the solution obtained by the moving finite element method converges to a local minimizer of the total energy when time goes to *** global minimizer,once it is detected by the discrete scheme,approximates the continuous stationary solution in optimal *** examples for a linear diffusion equation and a nonlinear Allen-Cahn equation are given to verify the analytical results.
We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral e...
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We propose Monte Carlo Nonlocal physics-informed neural networks(MC-Nonlocal-PINNs),which are a generalization of MC-fPINNs in *** et al.(*** ***.400(2022),115523)for solving general nonlocal models such as integral equations and nonlocal *** to MC-fPINNs,our MC-Nonlocal-PINNs handle nonlocal operators in a Monte Carlo way,resulting in a very stable approach for high dimensional *** present a variety of test problems,including high dimensional Volterra type integral equations,hypersingular integral equations and nonlocal PDEs,to demonstrate the effectiveness of our approach.
作者：
Xiaoying DaiLiwei ZhangAihui ZhouLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure *** this paper,we propose and analyze a class of iteration schemes for the di...
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To obtain convergent numerical approximations without using any orthogonalization operations is of great importance in electronic structure *** this paper,we propose and analyze a class of iteration schemes for the discretized Kohn-Sham Density Functional Theory model,with which the iterative approximations are guaranteed to converge to the Kohn-Sham orbitals without any orthogonalization as long as the initial orbitals are orthogonal and the time step sizes are given *** addition,we present a feasible and efficient approach to get suitable time step sizes and report some numerical experiments to validate our theory.
In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of ...
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In this paper,we develop a new sixth-order WENO scheme by adopting a convex combina-tion of a sixth-order global reconstruction and four low-order local *** the classical WENO schemes,the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals ***,a very simple smoothness indicator for the global stencil is *** new scheme can achieve sixth-order accuracy in smooth *** tests in some one-and two-dimensional bench-mark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme,and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.
作者：
Xie, PengchengState Key Laboratory of Scientific and Engineering Computing
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences ZhongGuanCun East Road No. 55 Beijing China
Optimization methods play a crucial role in various fields and applications. In some optimization problems, the derivative information of the objective function is unavailable. Such black-box optimization problems nee...
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