Because ambient seismic noise provides estimated Green’s function （EGF） between two sites with high accuracy, Rayleigh wave propagation along the path connecting the two sites is well resolved. Therefore, earthquak...Because ambient seismic noise provides estimated Green’s function （EGF） between two sites with high accuracy, Rayleigh wave propagation along the path connecting the two sites is well resolved. Therefore, earthquakes which are close to one seismic station can be well located with calibration extracting from EGF. We test two algorithms in locating the 1998 Zhangbei earthquake, one algorithm is waveform-based, and the other is traveltime-based. We first compute EGF between station ZHB （a station about 40 km away from the epicenter） and five IC/IRIS stations. With the waveform-based approach, we calculate 1D synthetic single-force Green’s functions between ZHB and other four stations, and obtain traveltime corrections by correlating synthetic Green’s functions with EGFs in period band of 10–30 s. Then we locate the earthquake by minimizing the differential travel times between observed earthquake waveform and the 1D synthetic earthquake waveforms computed with focal mechanism provided by Global CMT after traveltime correction from EGFs. This waveform-based approach yields a location which error is about 13 km away from the location observed with InSAR. With the traveltime-based approach, we begin with measuring group velocity from EGFs as well as group arrival time on observed earthquake waveforms, and then locate the earthquake by minimizing the difference between observed group arrival time and arrival time measured on EGFs. This traveltime-based approach yields accuracy of 3 km, Therefore it is feasible to achieve GT5 （ground truth location with accuracy 5 km） with ambient seismic noises. The less accuracy of the waveform-based approach was mainly caused by uncertainty of focal mechanism.展开更多
Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have ...Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.展开更多
Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems us...Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency.We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger equation.For several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low errors.The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.展开更多
The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordina...The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains： a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.展开更多
In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. T...In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized aJgorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.展开更多
基金supported by Chinese Acadmy of Sciences Fund(No.KCZX-YW-116-1)Joint Seismological Science Fundation of China (Nos.20080878 and 200708035)
文摘Because ambient seismic noise provides estimated Green’s function （EGF） between two sites with high accuracy, Rayleigh wave propagation along the path connecting the two sites is well resolved. Therefore, earthquakes which are close to one seismic station can be well located with calibration extracting from EGF. We test two algorithms in locating the 1998 Zhangbei earthquake, one algorithm is waveform-based, and the other is traveltime-based. We first compute EGF between station ZHB （a station about 40 km away from the epicenter） and five IC/IRIS stations. With the waveform-based approach, we calculate 1D synthetic single-force Green’s functions between ZHB and other four stations, and obtain traveltime corrections by correlating synthetic Green’s functions with EGFs in period band of 10–30 s. Then we locate the earthquake by minimizing the differential travel times between observed earthquake waveform and the 1D synthetic earthquake waveforms computed with focal mechanism provided by Global CMT after traveltime correction from EGFs. This waveform-based approach yields a location which error is about 13 km away from the location observed with InSAR. With the traveltime-based approach, we begin with measuring group velocity from EGFs as well as group arrival time on observed earthquake waveforms, and then locate the earthquake by minimizing the difference between observed group arrival time and arrival time measured on EGFs. This traveltime-based approach yields accuracy of 3 km, Therefore it is feasible to achieve GT5 （ground truth location with accuracy 5 km） with ambient seismic noises. The less accuracy of the waveform-based approach was mainly caused by uncertainty of focal mechanism.
文摘Artificial Neural Network(ANN)has become a powerful tool in the field of scientific research with its powerful information encapsulation ability and convenient variational optimization method.In particular,there have been many recent advances in computational physics to solve variational problems.Deep Neural Network(DNN)is used to represent the wave function to solve quantum many-body problems using variational optimization.In this work we used a new Physics-Informed Neural Network(PINN)to represent the Cumulative Distribution Function(CDF)of some classical problems in quantum mechanics and to obtain their ground state wave function and ground state energy through the CDF.By benchmarking against the exact solution,the error of the results can be controlled at a very low level.This new network architecture and optimization method can provide a new choice for solving quantum many-body problems.
基金Supported by the National Natural Science Foundation of China(12035006,12075098)the Natural Science Foundation of Hubei Province(2019CFB563)+1 种基金the Hubei Province Department of Education(D20201108)Hubei Province Department of Science and Technology(2021BLB171)。
文摘Deep neural networks(DNNs)and auto differentiation have been widely used in computational physics to solve variational problems.When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization,various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency.We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function(CDF)F(x)=ʃ^(x)_(-∞)Ψ*Ψdx',.Using this constrained neural network to represent the variational wave function,we solve Schrodinger equations using auto-differentiation and stochastic gradient descent(SGD)by minimizing the violation of the trial wave function(x)to the Schrodinger equation.For several classical problems in quantum mechanics,we obtain their ground state wave function and energy with very low errors.The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.
文摘The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains： a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.
基金The project supported by National Natural Science Foundation of China under Grant No. 10147207, the Natural Science Foundation of Chongqing Science and Technology Committee under Grant No. 2005BB8267, and the Fundamental Research Foundation of Chongqing Education Committee under Grant No. KJ060813
文摘In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized aJgorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.
