In this work,a direct discontinuous Galerkin(DDG)method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow,where the DDG approach i...In this work,a direct discontinuous Galerkin(DDG)method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow,where the DDG approach is used to discretize viscous and heat fluxes.A strong residual-based artificial viscosity(AV)technique is proposed to be applied in the DDG framework to handle shock waves and layer structures appearing in transonic or supersonic flow,which promotes convergence and robustness.Moreover,the AV term is added to classical BR2 methods for comparison.A number of 2-D and 3-D benchmarks such as airfoils,wings,and a full aircraft are presented to assess the performance of the DDG framework with the strong residualbased AV term for solving the two dimensional and three dimensional Navier-Stokes equations.The proposed framework provides an alternative robust and efficient approach for numerically simulating the multi-dimensional compressible Navier-Stokes equations for transonic or supersonic flow.展开更多
This paper suggests a modified serial correlation test for linear panel data models, which is based on the parameter estimates for an artificial autoregression modeled by differencing and centering residual vectors. S...This paper suggests a modified serial correlation test for linear panel data models, which is based on the parameter estimates for an artificial autoregression modeled by differencing and centering residual vectors. Specifically, the differencing operator over the time index and the centering operator over the individual index are, respectively, used to eliminate the potential individual effects and time effects so that the resultant serial correlation test is robust to the two potential effects. Clearly, the test is also robust to the potential correlation between the covariates and the random effects. The test is asymptotically chi-squared distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The finite sample properties of the test are investigated by means of Monte Carlo simulation experiments, and a real data example is analyzed for illustration.展开更多
Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the los...Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.展开更多
For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stab...For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r（Ω） norm and that of the pressure in the L r＇ （Ω） （1/r ＋ 1/r＇ = 1）. The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.展开更多
This paper proposes an innovative framework for medium-term wind power forecasting,employing a robust,multi-module Artificial Intelligence approach to improve prediction accuracy and reliability over extended horizons...This paper proposes an innovative framework for medium-term wind power forecasting,employing a robust,multi-module Artificial Intelligence approach to improve prediction accuracy and reliability over extended horizons.The framework consists of three key components:an internal–external learning process,a vertical–horizontal learning process,and a residual-based robust forecasting method.The internal–external process combines Variational Mode Decomposition with a stacked N-BEATS model,achieving stable and accurate forecasts across nearly 200 time steps.The vertical–horizontal process integrates the Polar Lights Optimizer with Joint Opposite Selection and a regression model based on the bidirectional long short-term memory and the gated recurrent unit,enabling efficient hyperparameter optimization and yielding a determination coefficient above 0.9996 for training data and a normalized root mean square error of 0.2448 for test data.We compared our proposed method with nine classical and state-of-the-art techniques and found that it delivers higher accuracy in medium-term prediction,extending to nearly 200 steps.The residual-based method addresses uncertainties by generating 95%confidence intervals,enhancing the model’s robustness in practical applications.By simulating real-world conditions,this framework provides reliable medium-term forecasts,making it an effective tool for renewable energy system dispatch and precise error control.展开更多
Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derive...Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.展开更多
This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to as...This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial autoregression modeled by centering and differencing residuals. The test can be shown to asymptotically chisquare distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects. Monte Carlo simulations are carried out for illustration.展开更多
基金support of National Natural Science Foundation of China(No.12001031)China Postdoctoral Science Foundation(No.2020M680284)National Numerical Wind Tunnel Project.
文摘In this work,a direct discontinuous Galerkin(DDG)method with artificial viscosity is developed to solve the compressible Navier-Stokes equations for simulating the transonic or supersonic flow,where the DDG approach is used to discretize viscous and heat fluxes.A strong residual-based artificial viscosity(AV)technique is proposed to be applied in the DDG framework to handle shock waves and layer structures appearing in transonic or supersonic flow,which promotes convergence and robustness.Moreover,the AV term is added to classical BR2 methods for comparison.A number of 2-D and 3-D benchmarks such as airfoils,wings,and a full aircraft are presented to assess the performance of the DDG framework with the strong residualbased AV term for solving the two dimensional and three dimensional Navier-Stokes equations.The proposed framework provides an alternative robust and efficient approach for numerically simulating the multi-dimensional compressible Navier-Stokes equations for transonic or supersonic flow.
基金Supported by the National Nature Science Foundation of China(Grant No.11001238)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103326120002)+3 种基金the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities(Grant No.13JJD910002)the National Bureau of statistics of key projects(Grant No.2012LZ023)the Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)the Center for Studies of Modern Business Zhejiang Gongshang University in the key research base for humanities and social Sciences of the Ministry of Education(Grant No.12JDSM09YB)
文摘This paper suggests a modified serial correlation test for linear panel data models, which is based on the parameter estimates for an artificial autoregression modeled by differencing and centering residual vectors. Specifically, the differencing operator over the time index and the centering operator over the individual index are, respectively, used to eliminate the potential individual effects and time effects so that the resultant serial correlation test is robust to the two potential effects. Clearly, the test is also robust to the potential correlation between the covariates and the random effects. The test is asymptotically chi-squared distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The finite sample properties of the test are investigated by means of Monte Carlo simulation experiments, and a real data example is analyzed for illustration.
基金Project supported by the Key National Natural Science Foundation of China(Grant No.62136005)the National Natural Science Foundation of China(Grant Nos.61922087,61906201,and 62006238)。
文摘Physics-informed neural networks(PINNs)have become an attractive machine learning framework for obtaining solutions to partial differential equations(PDEs).PINNs embed initial,boundary,and PDE constraints into the loss function.The performance of PINNs is generally affected by both training and sampling.Specifically,training methods focus on how to overcome the training difficulties caused by the special PDE residual loss of PINNs,and sampling methods are concerned with the location and distribution of the sampling points upon which evaluations of PDE residual loss are accomplished.However,a common problem among these original PINNs is that they omit special temporal information utilization during the training or sampling stages when dealing with an important PDE category,namely,time-dependent PDEs,where temporal information plays a key role in the algorithms used.There is one method,called Causal PINN,that considers temporal causality at the training level but not special temporal utilization at the sampling level.Incorporating temporal knowledge into sampling remains to be studied.To fill this gap,we propose a novel temporal causality-based adaptive sampling method that dynamically determines the sampling ratio according to both PDE residual and temporal causality.By designing a sampling ratio determined by both residual loss and temporal causality to control the number and location of sampled points in each temporal sub-domain,we provide a practical solution by incorporating temporal information into sampling.Numerical experiments of several nonlinear time-dependent PDEs,including the Cahn–Hilliard,Korteweg–de Vries,Allen–Cahn and wave equations,show that our proposed sampling method can improve the performance.We demonstrate that using such a relatively simple sampling method can improve prediction performance by up to two orders of magnitude compared with the results from other methods,especially when points are limited.
基金Project supported by the Key Technology Research and Development Program of Sichuan Province of China(No.05GG006-006-2)
文摘For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r（Ω） norm and that of the pressure in the L r＇ （Ω） （1/r ＋ 1/r＇ = 1）. The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.
基金supported by the Science and Technology Foundation of State Grid Corporation of China 5108-202319067A-1-1-ZN.
文摘This paper proposes an innovative framework for medium-term wind power forecasting,employing a robust,multi-module Artificial Intelligence approach to improve prediction accuracy and reliability over extended horizons.The framework consists of three key components:an internal–external learning process,a vertical–horizontal learning process,and a residual-based robust forecasting method.The internal–external process combines Variational Mode Decomposition with a stacked N-BEATS model,achieving stable and accurate forecasts across nearly 200 time steps.The vertical–horizontal process integrates the Polar Lights Optimizer with Joint Opposite Selection and a regression model based on the bidirectional long short-term memory and the gated recurrent unit,enabling efficient hyperparameter optimization and yielding a determination coefficient above 0.9996 for training data and a normalized root mean square error of 0.2448 for test data.We compared our proposed method with nine classical and state-of-the-art techniques and found that it delivers higher accuracy in medium-term prediction,extending to nearly 200 steps.The residual-based method addresses uncertainties by generating 95%confidence intervals,enhancing the model’s robustness in practical applications.By simulating real-world conditions,this framework provides reliable medium-term forecasts,making it an effective tool for renewable energy system dispatch and precise error control.
基金The research is SUpported by the NatlOllal Science Foundation of China(No.10371096)
文摘Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.
基金Supported by the National Natural Science Foundation of China(No.11671263)
文摘This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial autoregression modeled by centering and differencing residuals. The test can be shown to asymptotically chisquare distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects. Monte Carlo simulations are carried out for illustration.
