The Experts below are selected from a list of 24 Experts worldwide ranked by ideXlab platform

Travis S Waller - One of the best experts on this subject based on the ideXlab platform.

  • maximum entropy method for subnetwork origin destination trip matrix estimation
    Transportation Research Record, 2010
    Co-Authors: Kara M Kockelman, Travis S Waller
    Abstract:

    In the context of sketch planning, a simplified network (i.e., an abstract network or subnetwork) model is expected to accurately approximate travel demand patterns and level-of-service attributes obtained from its full-network counterpart. A data prerequisite in this approximation process is the trip matrix of the simplified network. This paper discusses a maximum entropy method for the subnetwork trip matrix estimation problem, relying only on link flow rates estimated with the use of full-network traffic assignment or as observed link-level vehicle counts. A linearization algorithm of the Frank-Wolfe type is devised for problem solutions in which a column-generation approach is used iteratively to solve the Linearized Subproblem without path enumeration. Encouraging results from sample applications of different size and topology suggest that this method holds much promise for generating trip matrices that can be used to evaluate traffic flow patterns under various network changes.

  • A MAXIMUM ENTROPY METHOD FOR SUBNETWORK ORIGIN-DESTINATION TRIP MATRIX ESTIMATION
    2010
    Co-Authors: Chi Xie, Kara M Kockelman, Travis S Waller
    Abstract:

    In the context of sketch planning, it is expected that a simplified network (i.e., an abstracted network or subnetwork) model can accurately approximate the travel demand patterns and levelof-service attributes obtained from its full-network counterpart. A data prerequisite in this approximation process is the trip matrix of the simplified network. This paper discusses a maximum entropy method for the subnetwork trip matrix estimation problem, relying only on link flow rates (estimated via full-network traffic assignment or as observed link-level vehicle counts). A linearization algorithm of the Frank-Wolfe type is devised for problem solutions, in which a column generation approach is iteratively used to solve the Linearized Subproblem without path enumeration. Encouraging results from a numerical example suggest that this method holds much promise for generating trip matrices that can be used to evaluate traffic flo

Kara M Kockelman - One of the best experts on this subject based on the ideXlab platform.

  • maximum entropy method for subnetwork origin destination trip matrix estimation
    Transportation Research Record, 2010
    Co-Authors: Kara M Kockelman, Travis S Waller
    Abstract:

    In the context of sketch planning, a simplified network (i.e., an abstract network or subnetwork) model is expected to accurately approximate travel demand patterns and level-of-service attributes obtained from its full-network counterpart. A data prerequisite in this approximation process is the trip matrix of the simplified network. This paper discusses a maximum entropy method for the subnetwork trip matrix estimation problem, relying only on link flow rates estimated with the use of full-network traffic assignment or as observed link-level vehicle counts. A linearization algorithm of the Frank-Wolfe type is devised for problem solutions in which a column-generation approach is used iteratively to solve the Linearized Subproblem without path enumeration. Encouraging results from sample applications of different size and topology suggest that this method holds much promise for generating trip matrices that can be used to evaluate traffic flow patterns under various network changes.

  • A MAXIMUM ENTROPY METHOD FOR SUBNETWORK ORIGIN-DESTINATION TRIP MATRIX ESTIMATION
    2010
    Co-Authors: Chi Xie, Kara M Kockelman, Travis S Waller
    Abstract:

    In the context of sketch planning, it is expected that a simplified network (i.e., an abstracted network or subnetwork) model can accurately approximate the travel demand patterns and levelof-service attributes obtained from its full-network counterpart. A data prerequisite in this approximation process is the trip matrix of the simplified network. This paper discusses a maximum entropy method for the subnetwork trip matrix estimation problem, relying only on link flow rates (estimated via full-network traffic assignment or as observed link-level vehicle counts). A linearization algorithm of the Frank-Wolfe type is devised for problem solutions, in which a column generation approach is iteratively used to solve the Linearized Subproblem without path enumeration. Encouraging results from a numerical example suggest that this method holds much promise for generating trip matrices that can be used to evaluate traffic flo

Bergou, El Houcine - One of the best experts on this subject based on the ideXlab platform.

  • Méthodes numériques pour les problèmes des moindres carrés, avec application à l'assimilation de données
    École Doctorale Mathématiques Informatique et Télécommunications (Toulouse);142547247, 2014
    Co-Authors: Bergou, El Houcine
    Abstract:

    L'algorithme de Levenberg-Marquardt (LM) est parmi les algorithmes les plus populaires pour la résolution des problèmes des moindres carrés non linéaire. Motivés par la structure des problèmes de l'assimilation de données, nous considérons dans cette thèse l'extension de l'algorithme LM aux situations dans lesquelles le sous problème linéarisé, qui a la forme min||Ax - b ||^2, est résolu de façon approximative, et/ou les données sont bruitées et ne sont précises qu'avec une certaine probabilité. Sous des hypothèses appropriées, on montre que le nouvel algorithme converge presque sûrement vers un point stationnaire du premier ordre. Notre approche est appliquée à une instance dans l'assimilation de données variationnelles où les modèles stochastiques du gradient sont calculés par le lisseur de Kalman d'ensemble (EnKS). On montre la convergence dans L^p de l'EnKS vers le lisseur de Kalman, quand la taille de l'ensemble tend vers l'infini. On montre aussi la convergence de l'approche LM-EnKS, qui est une variante de l'algorithme de LM avec l'EnKS utilisé comme solveur linéaire, vers l'algorithme classique de LM ou le sous problème est résolu de façon exacte. La sensibilité de la méthode de décomposition en valeurs singulières tronquée est étudiée. Nous formulons une expression explicite pour le conditionnement de la solution des moindres carrés tronqués. Cette expression est donnée en termes de valeurs singulières de A et les coefficients de Fourier de b. ABSTRACT : The Levenberg-Marquardt algorithm (LM) is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this thesis the extension of the LM algorithm to the scenarios where the Linearized least squares Subproblems, of the form min||Ax - b ||^2, are solved inexactly and/or the gradient model is noisy and accurate only within a certain probability. Under appropriate assumptions, we show that the modified algorithm converges globally and almost surely to a first order stationary point. Our approach is applied to an instance in variational data assimilation where stochastic models of the gradient are computed by the so-called ensemble Kalman smoother (EnKS). A convergence proof in L^p of EnKS in the limit for large ensembles to the Kalman smoother is given. We also show the convergence of LM-EnKS approach, which is a variant of the LM algorithm with EnKS as a linear solver, to the classical LM algorithm where the Linearized Subproblem is solved exactly. The sensitivity of the trucated sigular value decomposition method to solve the Linearized subprobems is studied. We formulate an explicit expression for the condition number of the truncated least squares solution. This expression is given in terms of the singular values of A and the Fourier coefficients of b

  • Numerical methods for least squares problems with application to data assimilation
    2014
    Co-Authors: Bergou, El Houcine
    Abstract:

    The Levenberg-Marquardt algorithm (LM) is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this thesis the extension of the LM algorithm to the scenarios where the Linearized least squares Subproblems, of the form min||Ax - b ||^2, are solved inexactly and/or the gradient model is noisy and accurate only within a certain probability. Under appropriate assumptions, we show that the modified algorithm converges globally and almost surely to a first order stationary point. Our approach is applied to an instance in variational data assimilation where stochastic models of the gradient are computed by the so-called ensemble Kalman smoother (EnKS). A convergence proof in L^p of EnKS in the limit for large ensembles to the Kalman smoother is given. We also show the convergence of LM-EnKS approach, which is a variant of the LM algorithm with EnKS as a linear solver, to the classical LM algorithm where the Linearized Subproblem is solved exactly. The sensitivity of the trucated sigular value decomposition method to solve the Linearized subprobems is studied. We formulate an explicit expression for the condition number of the truncated least squares solution. This expression is given in terms of the singular values of A and the Fourier coefficients of b

  • Numerical methods for least squares problems with application to data assimilation
    2014
    Co-Authors: Bergou, El Houcine
    Abstract:

    L'algorithme de Levenberg-Marquardt (LM) est parmi les algorithmes les plus populaires pour la résolution des problèmes des moindres carrés non linéaire. Motivés par la structure des problèmes de l'assimilation de données, nous considérons dans cette thèse l'extension de l'algorithme LM aux situations dans lesquelles le sous problème linéarisé, qui a la forme min||Ax - b ||^2, est résolu de façon approximative, et/ou les données sont bruitées et ne sont précises qu'avec une certaine probabilité. Sous des hypothèses appropriées, on montre que le nouvel algorithme converge presque sûrement vers un point stationnaire du premier ordre. Notre approche est appliquée à une instance dans l'assimilation de données variationnelles où les modèles stochastiques du gradient sont calculés par le lisseur de Kalman d'ensemble (EnKS). On montre la convergence dans L^p de l'EnKS vers le lisseur de Kalman, quand la taille de l'ensemble tend vers l'infini. On montre aussi la convergence de l'approche LM-EnKS, qui est une variante de l'algorithme de LM avec l'EnKS utilisé comme solveur linéaire, vers l'algorithme classique de LM ou le sous problème est résolu de façon exacte. La sensibilité de la méthode de décomposition en valeurs singulières tronquée est étudiée. Nous formulons une expression explicite pour le conditionnement de la solution des moindres carrés tronqués. Cette expression est donnée en termes de valeurs singulières de A et les coefficients de Fourier de b.The Levenberg-Marquardt algorithm (LM) is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this thesis the extension of the LM algorithm to the scenarios where the Linearized least squares Subproblems, of the form min||Ax - b ||^2, are solved inexactly and/or the gradient model is noisy and accurate only within a certain probability. Under appropriate assumptions, we show that the modified algorithm converges globally and almost surely to a first order stationary point. Our approach is applied to an instance in variational data assimilation where stochastic models of the gradient are computed by the so-called ensemble Kalman smoother (EnKS). A convergence proof in L^p of EnKS in the limit for large ensembles to the Kalman smoother is given. We also show the convergence of LM-EnKS approach, which is a variant of the LM algorithm with EnKS as a linear solver, to the classical LM algorithm where the Linearized Subproblem is solved exactly. The sensitivity of the trucated sigular value decomposition method to solve the Linearized subprobems is studied. We formulate an explicit expression for the condition number of the truncated least squares solution. This expression is given in terms of the singular values of A and the Fourier coefficients of b

Chi Xie - One of the best experts on this subject based on the ideXlab platform.

  • A MAXIMUM ENTROPY METHOD FOR SUBNETWORK ORIGIN-DESTINATION TRIP MATRIX ESTIMATION
    2010
    Co-Authors: Chi Xie, Kara M Kockelman, Travis S Waller
    Abstract:

    In the context of sketch planning, it is expected that a simplified network (i.e., an abstracted network or subnetwork) model can accurately approximate the travel demand patterns and levelof-service attributes obtained from its full-network counterpart. A data prerequisite in this approximation process is the trip matrix of the simplified network. This paper discusses a maximum entropy method for the subnetwork trip matrix estimation problem, relying only on link flow rates (estimated via full-network traffic assignment or as observed link-level vehicle counts). A linearization algorithm of the Frank-Wolfe type is devised for problem solutions, in which a column generation approach is iteratively used to solve the Linearized Subproblem without path enumeration. Encouraging results from a numerical example suggest that this method holds much promise for generating trip matrices that can be used to evaluate traffic flo

Mustonen Lauri - One of the best experts on this subject based on the ideXlab platform.

  • Numerical study of a parametric parabolic equation and a related inverse boundary value problem
    'IOP Publishing', 2016
    Co-Authors: Mustonen Lauri
    Abstract:

    We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any Linearized Subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.Comment: 19 pages, 5 figure