The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computin...The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computing do not satisfy the stationary assumption.To overcome the difficulty,we propose a normalizing field flow induced two-stage stochastic homogenization method to efficiently solve the random elliptic problem with non-stationary coefficients.By applying the two-stage stochastic homogenization method,the original elliptic equation with random and fast oscillatory coefficients is approximated as an equivalent elliptic equation,where the equivalent coefficients are obtained by solving a set of cell problems.Without the stationary assumption,the number of cell problems is large and the corresponding computational cost is high.To improve the efficiency,we apply the normalizing field flow model to learn a reference Gaussian field for the random equivalent coefficients based on a small amount of data,which is obtained by solving the cell problems with the finite element method.Numerical results demonstrate that the newly proposed method is efficient and accurate in tackling high dimensional partial differential equations in composite materials with complex random microstructures.展开更多
Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning me...Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.展开更多
Simulation technology for shape casting at macro-scale has been successfully put into engineer- ing application in a number of casting plants and as a result the quality of castings is assured, the research and deve...Simulation technology for shape casting at macro-scale has been successfully put into engineer- ing application in a number of casting plants and as a result the quality of castings is assured, the research and development time is shortened, and the manufacturing cost is greatly saved as well. In this paper, mod- eling and simulation technologies of solidification process of shape casting at microstructure-scale, espe- cially deterministic, cellular automaton, and phase field models are studied and reviewed.展开更多
The spectral representation method (SRM) is most widely used in simulating the stochastic field.The proper orthogonal decomposition (POD) based SRM is an important form.This paper investigates the approximate approach...The spectral representation method (SRM) is most widely used in simulating the stochastic field.The proper orthogonal decomposition (POD) based SRM is an important form.This paper investigates the approximate approaches to the POD-based SRM in simulating two typical problems,i.e.,the seismic ground motion and wind velocity fields simulations.Then,the accuracy resulting from the power spectral density matrix-based POD method (PSRM) is compared to that of the coherency matrix-based POD method (CPSRM).It is concluded that the CPSRM maintains a much higher accuracy than the PSRM.In the CPSRM,the linear interpolation of eigenvectors and third-order polynomial interpolation of eigenvalues can be accepted to attain high accuracy;the linearly distributed interpolation nodes are effective in the ground motions simulation;however,the exponentially distributed interpolation nodes are effective in the wind velocity simulation.展开更多
Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be charact...Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method （SRM） and the Static Transformation Method （STM）. Polynomial and Exponential transformation functions （PSTM and ESTM） are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.展开更多
基金supported by the National Natural Science Foundation of China grant(12131002,51739007,12271409)Strategic Priority Research Program of the Chinese Academy of Sciences(XDC06030101)+2 种基金the National Key R&D Program of China with the grant(2020YFA-0713603)Natural Science Foundation of Shanghai grant(21ZR1465800)the Interdisciplinary Project in Ocean Research of Tongji University and the Fundamental Research Funds for the Central Universities..
文摘The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computing do not satisfy the stationary assumption.To overcome the difficulty,we propose a normalizing field flow induced two-stage stochastic homogenization method to efficiently solve the random elliptic problem with non-stationary coefficients.By applying the two-stage stochastic homogenization method,the original elliptic equation with random and fast oscillatory coefficients is approximated as an equivalent elliptic equation,where the equivalent coefficients are obtained by solving a set of cell problems.Without the stationary assumption,the number of cell problems is large and the corresponding computational cost is high.To improve the efficiency,we apply the normalizing field flow model to learn a reference Gaussian field for the random equivalent coefficients based on a small amount of data,which is obtained by solving the cell problems with the finite element method.Numerical results demonstrate that the newly proposed method is efficient and accurate in tackling high dimensional partial differential equations in composite materials with complex random microstructures.
基金Supported by the Natural Science Foundation of China under Grant No.11875082
文摘Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.
基金Supported by the National Key Basic Research and Development (973) Program of China (No. G20000672083)
文摘Simulation technology for shape casting at macro-scale has been successfully put into engineer- ing application in a number of casting plants and as a result the quality of castings is assured, the research and development time is shortened, and the manufacturing cost is greatly saved as well. In this paper, mod- eling and simulation technologies of solidification process of shape casting at microstructure-scale, espe- cially deterministic, cellular automaton, and phase field models are studied and reviewed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51278382,90815020)the Chang Jiang Scholars Program and the Innovative Research Team Program of the Ministry of Education of China (Grant No. IRT1125)the "111" Project (Grant No.B13024)
文摘The spectral representation method (SRM) is most widely used in simulating the stochastic field.The proper orthogonal decomposition (POD) based SRM is an important form.This paper investigates the approximate approaches to the POD-based SRM in simulating two typical problems,i.e.,the seismic ground motion and wind velocity fields simulations.Then,the accuracy resulting from the power spectral density matrix-based POD method (PSRM) is compared to that of the coherency matrix-based POD method (CPSRM).It is concluded that the CPSRM maintains a much higher accuracy than the PSRM.In the CPSRM,the linear interpolation of eigenvectors and third-order polynomial interpolation of eigenvalues can be accepted to attain high accuracy;the linearly distributed interpolation nodes are effective in the ground motions simulation;however,the exponentially distributed interpolation nodes are effective in the wind velocity simulation.
基金National Natural Science Foundation of China under Grant Nos.51278160,51478155,51378147
文摘Stochastic simulation is an important means of acquiring fluctuating wind pressures for wind induced response analyses in structural engineering. The wind pressure acting on a large-span space structure can be characterized as a stationary non-Gaussian field. This paper reviews several simulation algorithms related to the Spectral Representation Method （SRM） and the Static Transformation Method （STM）. Polynomial and Exponential transformation functions （PSTM and ESTM） are discussed. Deficiencies in current algorithms, with respect to accuracy, stability and efficiency, are analyzed, and the algorithms are improved for better practical application. In order to verify the improved algorithm, wind pressure fields on a large-span roof are simulated and compared with wind tunnel data. The simulation results fit well with the wind tunnel data, and the algorithm accuracy, stability and efficiency are shown to be better than those of current algorithms.
