Massive data from observations,experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models.We present a novel me...Massive data from observations,experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models.We present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussianα-stable Lévy noise.More explicitly,firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers–Moyal formulas.Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process.Three examples are then given to demonstrate the feasibility.This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.展开更多
The dynamical modeling of projectile systems with sufficient accuracy is of great difficulty due to high-dimensional space and various perturbations.With the rapid development of data science and scientific tools of m...The dynamical modeling of projectile systems with sufficient accuracy is of great difficulty due to high-dimensional space and various perturbations.With the rapid development of data science and scientific tools of measurement recently,there are numerous data-driven methods devoted to discovering governing laws from data.In this work,a data-driven method is employed to perform the modeling of the projectile based on the Kramers–Moyal formulas.More specifically,the four-dimensional projectile system is assumed as an It?stochastic differential equation.Then the least square method and sparse learning are applied to identify the drift coefficient and diffusion matrix from sample path data,which agree well with the real system.The effectiveness of the data-driven method demonstrates that it will become a powerful tool in extracting governing equations and predicting complex dynamical behaviors of the projectile.展开更多
We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenval...We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenvalue of the free fermion Dirac operator as same as the result by [Hajime Aoki, Satoshi Iso, and Kelichi Nagao, Phys. Rev.D67 (2003) 065018]. Meanwhile, we also give the eigenvalue of Dirac operator with U(1) Dirac monopole background.展开更多
Multi-soliton configurations of a Moyal-type noncommutative deformed modified 2＋1 chiral model have been constructed by dressing method several years ago. These configurations have no-scattering property. By making a...Multi-soliton configurations of a Moyal-type noncommutative deformed modified 2＋1 chiral model have been constructed by dressing method several years ago. These configurations have no-scattering property. By making a second-order pole in the dressing ansatz, two-soliton configurations with genuine soliton-soliton interaction were constructed after that. We go on in this paper to construct a large family of multi-soliton configurations with scattering property by using the noncom- mutative extension of B/icklund transformations defined by Dai and Terng in a recent paper展开更多
By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quant...By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .展开更多
基金the National Natural Science Foundation of China(Grant No.12172167)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)。
文摘Massive data from observations,experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these models.We present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussianα-stable Lévy noise.More explicitly,firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers–Moyal formulas.Then the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the process.Three examples are then given to demonstrate the feasibility.This approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.
基金the Six Talent Peaks Project in Jiangsu Province,China(Grant No.JXQC-002)。
文摘The dynamical modeling of projectile systems with sufficient accuracy is of great difficulty due to high-dimensional space and various perturbations.With the rapid development of data science and scientific tools of measurement recently,there are numerous data-driven methods devoted to discovering governing laws from data.In this work,a data-driven method is employed to perform the modeling of the projectile based on the Kramers–Moyal formulas.More specifically,the four-dimensional projectile system is assumed as an It?stochastic differential equation.Then the least square method and sparse learning are applied to identify the drift coefficient and diffusion matrix from sample path data,which agree well with the real system.The effectiveness of the data-driven method demonstrates that it will become a powerful tool in extracting governing equations and predicting complex dynamical behaviors of the projectile.
文摘We treat the Dirac operator on the Fuzzy sphere with the help of the generalized coherent state. It is shown that the derivatives can be constructed by Moyal product with symbol of the operator. We obtain the eigenvalue of the free fermion Dirac operator as same as the result by [Hajime Aoki, Satoshi Iso, and Kelichi Nagao, Phys. Rev.D67 (2003) 065018]. Meanwhile, we also give the eigenvalue of Dirac operator with U(1) Dirac monopole background.
基金The NSF(10671171)of Chinathe NSF(BK2007073) of Jiangsu Province,China
文摘Multi-soliton configurations of a Moyal-type noncommutative deformed modified 2＋1 chiral model have been constructed by dressing method several years ago. These configurations have no-scattering property. By making a second-order pole in the dressing ansatz, two-soliton configurations with genuine soliton-soliton interaction were constructed after that. We go on in this paper to construct a large family of multi-soliton configurations with scattering property by using the noncom- mutative extension of B/icklund transformations defined by Dai and Terng in a recent paper
基金This research work is supported by the National Natural Science Foundation of China.
文摘By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .
