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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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.
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.
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：
Shipeng MaoJiaao SunWendong XueNCMIS
LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences
University of Chinese Academy of SciencesBeijing 100049China
In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity resu...
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In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.
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：
Pengcong MuWeiying ZhengSchool of Mathematical Science
University of Chinese Academy of SciencesBeijing 100049China LSEC
NCMISInstitute of Computational Mathematics and Scientific ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China
In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion *** model consists of five nonlinear elliptic equations,and two of them describe quantum...
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In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion *** model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi *** propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction *** IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction ***,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi *** Poisson equation of electrical potential is solved with standard Lagrangian finite *** prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete *** experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.
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 work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar *** formulate the design problems as random PDE-constrained optimization pr...
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In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar *** formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random *** optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are *** evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the *** stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost *** numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random *** also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.
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