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.
By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are pre...
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By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and *** algorithms are highly *** first,a global solution is obtained on a coarse grid for all approaches by one of the iteration *** parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping *** subdomains can be achieved flexibly by a class of *** proposed algorithm is proved to be uniformly stable and ***,one numerical example is presented to confirm the theoretical findings.
Since the nonconforming finite elements(NFEs)play a significant role in approximating PDE eigenvalues from below,this paper develops a new and parallel two-level preconditioned Jacobi-Davidson(PJD)method for solving t...
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Since the nonconforming finite elements(NFEs)play a significant role in approximating PDE eigenvalues from below,this paper develops a new and parallel two-level preconditioned Jacobi-Davidson(PJD)method for solving the large scale discrete eigenvalue problems resulting from NFE discretization of 2mth(m=1.2)order elliptic eigenvalue *** a spectral projection on the coarse space and an overlapping domain decomposition(DD),a parallel preconditioned system can be solved in each iteration.A rigorous analysis reveals that the convergence rate of our two-level PJD method is optimal and *** results supporting our theory are given.
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.
In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a phys...
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In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a physics-informed neural network method combined with learning rate attenuation strategy to solve linear impulsive differential equations and nonlinear impulsive differential equations, respectively. For the linear impulsive differential equations, first, the interval is segmented according to the impulse points, and a single hidden layer neural network model is constructed, the weight parameters of the hidden layer are randomly set, the optimal output parameters, and solution of the first segment are obtained by the extreme learning machine algorithm, then we calculate the initial value of the second segment according to the jumping equation and the remaining segments are solved in turn in the same way. Although the single hidden layer neural network method proposed can solve linear equations with high accuracy, it is not suitable for solving nonlinear equations. Therefore, we propose the physics-informed neural network combined with a learning rate attenuation strategy to solve the nonlinear impulsive differential equations, then the Adam algorithm and L-BFGS algorithm are combined to find the optimal approximate solution of each segment. Numerical examples show that the single hidden layer neural network method with Legendre polynomials as the activation function and the physics-informed neural network method combined with learning rate attenuation strategy can solve linear and nonlinear impulsive differential equations with higher accuracy. Impact Statement-It is difficult to obtain the analytical solutions of impulsive differential equations because of the existence of impulse points, and the current numerical methods are complicated and demanding. In recent years, artificial neural network methods have been widely used due to its simplicity and efficie
Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefiel...
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Hydride precipitation in zirconium cladding materials can damage their integrity and *** temperature and material defects have a significant effect on the dynamic growth of *** this study,we have developed a phasefield model based on the assumption of elastic behaviour within a specific temperature range(613 K-653 K).This model allows us to study the influence of temperature and interfacial effects on the morphology,stress,and average growth rate of zirconium *** results suggest that changes in temperature and interfacial energy influence the length-to-thickness ratio and average growth rate of the hydride *** ultimate determinant of hydride orientation is the loss of interfacial coherency,primarily induced by interfacial dislocation defects and quantifiable by the mismatch degree *** escalation in interfacial coherency loss leads to a transition of hydride growth from horizontal to vertical,accompanied by the onset of redirection ***,redirection occurs at a critical mismatch level,denoted as qc,and remains unaffected by variations in temperature and interfacial ***,this redirection leads to an increase in the maximum stress,which may influence the direction of hydride crack *** research highlights the importance of interfacial coherency and provides valuable insights into the morphology and growth kinetics of hydrides in zirconium alloys.
The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aero...
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The Tungsten-Rhenium(W-Re) alloys,celebrated for their high melting point,strength at elevated temperatures,electrical resistivity,and radiation resistance,have been widely utilized in high-temperature components,aerospace,electronics,and nuclear *** constituents of the topologically close-packed(TCP) phases,the sigma phase(σ) and chi phase(χ) formed within W-Re alloys wield considerable influence on the mechanical properties and the stability of the *** calculations were utilized in the present work to explore the structural,thermodynamic,and electronic properties of both ordered and disordered configurations within the σ and χ phases,culminating in a systematic elucidation of the higher phase stability exhibited by the ordered *** is found that the bulk modulus of these two phases is directly proportional to the concentration of Re in the alloy,while the equilibrium volume is inversely *** thermodynamic parameters of the σ and χ phases are calculated via the mean-field potential *** similar trends observed in the isobaric heat capacity,enthalpy increment,and entropy change curves for these two phases suggest they possess comparable thermodynamic *** is noteworthy that the contribution of ionic vibrations predominantly affects the isobaric heat capacity,while the contribution of thermal electronic excitations increases linearly with *** the structure and thermodynamic properties of TCP phases in W-Re alloys at low temperatures has profound significance for optimizing material performance,microstructures features,establishing theoretical foundations,and predicting material behavior.
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.
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