Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water va...Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water vapor from 1300 nm to 1350 nm,the temperature probability distribution of nonuniform temperature distribution,for which a parabolic temperature profile is selected as an example in this paper,was retrieved by making the use of regularization methods.To examine the effectiveness of regularization methods,truncated singular value decomposition(TSVD),Tikhonov regularization and a revised Tikhonov regularization method were implemented to retrieve the temperature probability distribution.The results derived by using the three regularization methods were compared with that by using constrained linear least-square fitting.The results show that regularization methods not only generate closer temperature probability distributions to the original,but also are less sensitive to measurement noise.Particularly,the revised Tikhonov regularization method generate solutions in better agreement with the original ones than those obtained by using TSVD and Tikhonov regularization methods.The results obtained in this work can enrich the temperature distribution information,which is expected to play a more important role in combustion diagnosis.展开更多
Based on variational adjoint methods,theoretical analyses and numerical experiments are performed for retrievals of two-dimensional winds and related parameters from single-Doppler radar data in polar coordinates.In t...Based on variational adjoint methods,theoretical analyses and numerical experiments are performed for retrievals of two-dimensional winds and related parameters from single-Doppler radar data in polar coordinates.In the method,the reflectivity conservation equation is used as the governing equation and the mass continuity equation as a weak constraint.At the same time,the stable functional of regularization and background field are also introduced in the cost functional.Based on the ideal experiments with artificial data,real two-dimensional wind fields are retrieved with low-altitude data from the Nanjing Doppler Radar Station,and the results are encouraging and promising.展开更多
Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation （TV） model ...Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation （TV） model [11] designed for local inpainting and its improved version for large scale inpainting： the Curvature-Driven Diffusion （CDD） model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear partial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immediate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 （2005）, pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the original CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.展开更多
The Variational Optimization Analysis Method （VOAM） for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can he used efficiently in most cases. However, in the cases where there are h...The Variational Optimization Analysis Method （VOAM） for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can he used efficiently in most cases. However, in the cases where there are high frequency noises in 2-D flow field, it appears to be inefficient. In the present paper, based on Sasaki＇s VOAM, a Generalized Variational Optimization Analysis Method （GVOAM） was proposed with regularization ideas, which could deal well with flow fields containing high frequency noises. A numerical test shows that observational data can be both variationally optimized and filtered, and therefore the GVOAM is an efficient method.展开更多
The problem of finding a L^∞-bounded two-dimensional vector field whose divergence is given in L2 is discussed from the numerical viewpoint. A systematic way to find such a vector field is to introduce a non-smooth v...The problem of finding a L^∞-bounded two-dimensional vector field whose divergence is given in L2 is discussed from the numerical viewpoint. A systematic way to find such a vector field is to introduce a non-smooth variational problem involving a L^∞-norm. To solve this problem from calculus of variations, we use a method relying on a well- chosen augmented Lagrangian functional and on a mixed finite element approximation. An Uzawa algorithm allows to decouple the differential operators from the nonlinearities introduced by the L^∞-norm, and leads to the solution of a sequence of Stokes-like systems and of an infinite family of local nonlinear problems. A simpler method, based on a L2- regularization is also considered. Numerical experiments are performed, making use of appropriate numerical integration techniques when non-smooth data are considered; they allow to compare the merits of the two approaches discussed in this article and to show the ability of the related methods at capturing L^∞bounded solutions.展开更多
Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of param...Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic forecasts.In the absence of reliable information about transmission mechanisms of emerging infectious diseases,phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the disease.In this article,our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014e15 Ebola epidemic in West Africa.展开更多
The cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained con...The cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian.Then,based on this reformulation,we derive a variant of the(non-adaptive)CR provided a known Lipschitz constant for the Hessian and a variant of adaptive regularization with cubics(ARC).We show that the iteration complexity of our variants matches the best-known bounds for unconstrained minimization algorithms using first-and second-order information.Moreover,we show that the operation complexity of both of our variants also matches the state-of-the-art bounds in the literature.Numerical experiments on test problems from CUTEst collection show that the ARC based on our new subproblem reformulation is comparable to the existing algorithms.展开更多
基金support by the National Science Foundation for Distinguished Youth Scholars of China(Grant No.61225006)National Natural Science Foundation of China(Grant No.60972087)Natural Science Foundation of Beijing,China(Grant No.3112018).
文摘Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water vapor from 1300 nm to 1350 nm,the temperature probability distribution of nonuniform temperature distribution,for which a parabolic temperature profile is selected as an example in this paper,was retrieved by making the use of regularization methods.To examine the effectiveness of regularization methods,truncated singular value decomposition(TSVD),Tikhonov regularization and a revised Tikhonov regularization method were implemented to retrieve the temperature probability distribution.The results derived by using the three regularization methods were compared with that by using constrained linear least-square fitting.The results show that regularization methods not only generate closer temperature probability distributions to the original,but also are less sensitive to measurement noise.Particularly,the revised Tikhonov regularization method generate solutions in better agreement with the original ones than those obtained by using TSVD and Tikhonov regularization methods.The results obtained in this work can enrich the temperature distribution information,which is expected to play a more important role in combustion diagnosis.
基金supported by the National Key Technologies R and D Program of China during the 11th Five-year Plan Period(Grant No. 2008BAC37B03)
文摘Based on variational adjoint methods,theoretical analyses and numerical experiments are performed for retrievals of two-dimensional winds and related parameters from single-Doppler radar data in polar coordinates.In the method,the reflectivity conservation equation is used as the governing equation and the mass continuity equation as a weak constraint.At the same time,the stable functional of regularization and background field are also introduced in the cost functional.Based on the ideal experiments with artificial data,real two-dimensional wind fields are retrieved with low-altitude data from the Nanjing Doppler Radar Station,and the results are encouraging and promising.
基金a CONACYT (El Consejo Nacional de Ciencia y Tecnologia) scholarship from Mexico
文摘Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation （TV） model [11] designed for local inpainting and its improved version for large scale inpainting： the Curvature-Driven Diffusion （CDD） model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear partial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immediate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 （2005）, pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the original CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.
基金Project supported by the National Natural Science Foundation of China (Grant No :90411006) and the Association ofScience and Technology of Shanghai (Grant No :02DJ14032) .
文摘The Variational Optimization Analysis Method （VOAM） for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can he used efficiently in most cases. However, in the cases where there are high frequency noises in 2-D flow field, it appears to be inefficient. In the present paper, based on Sasaki＇s VOAM, a Generalized Variational Optimization Analysis Method （GVOAM） was proposed with regularization ideas, which could deal well with flow fields containing high frequency noises. A numerical test shows that observational data can be both variationally optimized and filtered, and therefore the GVOAM is an efficient method.
文摘The problem of finding a L^∞-bounded two-dimensional vector field whose divergence is given in L2 is discussed from the numerical viewpoint. A systematic way to find such a vector field is to introduce a non-smooth variational problem involving a L^∞-norm. To solve this problem from calculus of variations, we use a method relying on a well- chosen augmented Lagrangian functional and on a mixed finite element approximation. An Uzawa algorithm allows to decouple the differential operators from the nonlinearities introduced by the L^∞-norm, and leads to the solution of a sequence of Stokes-like systems and of an infinite family of local nonlinear problems. A simpler method, based on a L2- regularization is also considered. Numerical experiments are performed, making use of appropriate numerical integration techniques when non-smooth data are considered; they allow to compare the merits of the two approaches discussed in this article and to show the ability of the related methods at capturing L^∞bounded solutions.
基金Dr.Gerardo Chowell acknowledges financial support from NSF grant 1414374 as part of the joint NSF-NIH-USDA Ecology and Evolution of Infectious Diseases programUK Biotechnology and Biological Sciences Research Council grant BB/M008894/1 and NSF grant 1610429.
文摘Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic forecasts.In the absence of reliable information about transmission mechanisms of emerging infectious diseases,phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the disease.In this article,our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014e15 Ebola epidemic in West Africa.
基金supported in part by the National Natural Foundation of China(Nos.11801087 and 12171100).
文摘The cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian.Then,based on this reformulation,we derive a variant of the(non-adaptive)CR provided a known Lipschitz constant for the Hessian and a variant of adaptive regularization with cubics(ARC).We show that the iteration complexity of our variants matches the best-known bounds for unconstrained minimization algorithms using first-and second-order information.Moreover,we show that the operation complexity of both of our variants also matches the state-of-the-art bounds in the literature.Numerical experiments on test problems from CUTEst collection show that the ARC based on our new subproblem reformulation is comparable to the existing algorithms.
