结合2013年3月23-24日广西一次区域性强对流天气过程,运用常规观测资料、MICAPS实况资料和EC细网格数值预报资料计算准地转ω方程的两个主要强迫项:涡度平流的垂直差动项(简称"涡度平流项")和温度平流的拉普拉斯项(简称"...结合2013年3月23-24日广西一次区域性强对流天气过程,运用常规观测资料、MICAPS实况资料和EC细网格数值预报资料计算准地转ω方程的两个主要强迫项:涡度平流的垂直差动项(简称"涡度平流项")和温度平流的拉普拉斯项(简称"温度平流项")。结果表明,天气尺度的抬升运动主要是温度平流项的贡献,500 h Pa高空槽前的负变温造成了斜压性加强是抬升运动加强的主要原因,也是桂北强对流范围增大的主要原因。用ω方程结合数值预报回报的结果能较好地反映天气实况,说明上述方法在强对流天气预报中有一定的指导意义。展开更多
This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback...This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the solution.Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate.Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence.To address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients.Consequently,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible.Our method also provides a mechanism to focus on complex regions of the domain.Besides,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient methods.We apply our approach to solve various linear and non-linear PDEs.展开更多
Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/C...Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.展开更多
The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetri...The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
The energy-intensive industrial economy results in frequent Fog-Haze weather which increases the risk of influenza spread and brings new challenges for the prevention and control of influenza.Therefore,the study of sp...The energy-intensive industrial economy results in frequent Fog-Haze weather which increases the risk of influenza spread and brings new challenges for the prevention and control of influenza.Therefore,the study of spread mechanics and controlling strategies of influenza based on Fog-Haze will be scientifically meaningful.Considering that when the concentration of Fog-Haze is low,Fog-Haze contributes to the number of infectious individuals and Fog-Haze suppresses the transmission of the influenza virus when the concentration of Fog-Haze is high,we establish the Fog-Haze dynamics model.Then we prove the global existence and boundedness of the solution,and the global asymptotic stability of the solution is given by constructing a suitable Lyapunov functional.Under the Fog-Haze weather,we study the inffuenza virus transmission model that incorporates the incidence rate to reflect the Fog-Haze-dependent saturation effect and investigate the effect of Fog-Haze pollution on the transmission of influenza.We show that the basic reproduction number R_(0) determines the global dynamics of the system:if R_(0)<1,the disease-free equilibrium is global asymptotically stable;the unique endemic equilibrium is global asymptotically stable if R_(0)>1.Simulations are carried out to validate the theoretical results.Our study provides further understanding of the dynamics of Fog-Haze and the effect of Fog-Haze pollution on the transmission of influenza.展开更多
文摘结合2013年3月23-24日广西一次区域性强对流天气过程,运用常规观测资料、MICAPS实况资料和EC细网格数值预报资料计算准地转ω方程的两个主要强迫项:涡度平流的垂直差动项(简称"涡度平流项")和温度平流的拉普拉斯项(简称"温度平流项")。结果表明,天气尺度的抬升运动主要是温度平流项的贡献,500 h Pa高空槽前的负变温造成了斜压性加强是抬升运动加强的主要原因,也是桂北强对流范围增大的主要原因。用ω方程结合数值预报回报的结果能较好地反映天气实况,说明上述方法在强对流天气预报中有一定的指导意义。
文摘This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective function.However,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the solution.Our investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to navigate.Our findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder convergence.To address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated gradients.Consequently,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions feasible.Our method also provides a mechanism to focus on complex regions of the domain.Besides,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient methods.We apply our approach to solve various linear and non-linear PDEs.
基金supported by the National Natural Science Foundation of China(No.60874039)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(No.J50101)
文摘Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968.
文摘The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金supported by the National Natural Science Foundation of China (12171291,11601291,61873154)the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province (20200001)+5 种基金the Fundamental Research Program of Shanxi Province (20210302124018)the Shanxi Scholarship Council of China (HGKY2019004)the Scientific and Technological Innovation Programs (STIP)of Higher Education Institutions in Shanxi (2019L0082)the Program for the Outstanding Innovative Teams (OIT)of Higher Learning Institutions of Shanxithe Simons Foundation-Mathematics and Physical Sciences (523360)the 1331 Engineering Project of Shanxi Province.
文摘The energy-intensive industrial economy results in frequent Fog-Haze weather which increases the risk of influenza spread and brings new challenges for the prevention and control of influenza.Therefore,the study of spread mechanics and controlling strategies of influenza based on Fog-Haze will be scientifically meaningful.Considering that when the concentration of Fog-Haze is low,Fog-Haze contributes to the number of infectious individuals and Fog-Haze suppresses the transmission of the influenza virus when the concentration of Fog-Haze is high,we establish the Fog-Haze dynamics model.Then we prove the global existence and boundedness of the solution,and the global asymptotic stability of the solution is given by constructing a suitable Lyapunov functional.Under the Fog-Haze weather,we study the inffuenza virus transmission model that incorporates the incidence rate to reflect the Fog-Haze-dependent saturation effect and investigate the effect of Fog-Haze pollution on the transmission of influenza.We show that the basic reproduction number R_(0) determines the global dynamics of the system:if R_(0)<1,the disease-free equilibrium is global asymptotically stable;the unique endemic equilibrium is global asymptotically stable if R_(0)>1.Simulations are carried out to validate the theoretical results.Our study provides further understanding of the dynamics of Fog-Haze and the effect of Fog-Haze pollution on the transmission of influenza.
