The Experts below are selected from a list of 78909 Experts worldwide ranked by ideXlab platform
Benar Fux Svaiter - One of the best experts on this subject based on the ideXlab platform.
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A robust Kantorovich's theorem on the inexact Newton Method with relative residual error tolerance
Journal of Complexity, 2012Co-Authors: Orizon P. Ferreira, Benar Fux SvaiterAbstract:We prove that under semi-local assumptions, the inexact Newton Method with a fixed relative residual error tolerance converges Q-linearly to a zero of the nonlinear operator under consideration. Using this result we show that the Newton Method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on the Newton Method.
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A robust Kantorovich's theorem on inexact Newton Method with relative residual error tolerance
arXiv: Numerical Analysis, 2011Co-Authors: Orizon P. Ferreira, Benar Fux SvaiterAbstract:We prove that under semi-local assumptions, the inexact Newton Method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration. Using this result we show that Newton Method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on Newton Method.
Jean Virieux - One of the best experts on this subject based on the ideXlab platform.
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Full Waveform Inversion and the Truncated Newton Method
SIAM Review, 2017Co-Authors: Ludovic Métivier, Romain Brossier, Stéphane Operto, Jean VirieuxAbstract:Full waveform inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing the distance between predicted and recorded data. The predicted data are computed as the solution of a wave-propagation problem. Conventional numerical Methods for the solution of FWI problems are gradient-based Methods, such as the preconditioned steepest descent, the nonlinear conjugate gradient, or more recently the $l$-BFGS quasi-Newton algorithm. In this study, we investigate the desirability of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction, as it should help to mitigate finite-frequency effects and to better remove artifacts arising from multiscattered waves. For multiparameter reconstruction, the inverse Hessian operator also offers the possibility of better removing trade-offs due to coupling effects between parameter classes. The truncated Newton Method allows us to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through the conjugate gradient Method. The large-scale nature of FWI problems requires us, however, to carefully implement this Method to avoid prohibitive computational costs. First, this requires working in a matrix-free formalism and the capability of efficiently computing Hessian-vector products. For this purpose, we propose general second-order adjoint state formulas. Second, special attention must be paid to defining the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug--Toint Method, based on trust regions, and the Eisenstat and Walker stopping criterion, designed for a Method globalized by linesearch. We investigate the application of the truncated Newton Method to two case studies. The first is a standard case study in seismic imaging based on the Marmousi model. The second is inspired by a near-surface imaging problem for the reconstruction of high-velocity structures. In the latter case, we demonstrate that the presence of large amplitude multiscattered waves prevents standard Methods from converging, while the truncated Newton Method provides more reliable results.
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Full Waveform Inversion and the truncated Newton Method
SIAM Journal on Scientific Computing, 2013Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing a distance between predicted and recorded data. The predicted data is computed as the solution of a wave propagation problem. Conventional numerical Methods for the resolution of FWI problems are gradient-based Methods, such as the preconditioned steepest-descent, or more recently the l-BFGS quasi-Newton algorithm. In this study, we investigate the interest of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton Method allows one to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient Method. The large-scale nature of FWI problems requires however to carefully implement this Method to avoid prohibitive computational costs. First, this requires to work in a matrix-free formalism, and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be payed to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug-Toint Method, based on trust-regions, and the Eisenstat stopping criterion, designed for Method globalized by linesearch. We investigate the application of the truncated Newton Method to two test cases: the first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near-surface imaging problem for the reconstruction of high velocity structures. In the latter case, we demonstrate that the presence of large amplitude multi-scattered waves prevents standard Methods from converging while the truncated Newton Method provides more reliable results.
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Full Waveform Inversion and the Truncated Newton Method
SIAM Journal on Scientific Computing, 2013Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:ull waveform inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing the distance between predicted and recorded data. The predicted data are computed as the solution of a wave-propagation problem. Conventional numerical Methods for the resolution of FWI problems are gradient-based Methods, such as the preconditioned steepest descent, or more recently the $l$-BFGS quasi-Newton algorithm. In this study, we investigate the desirability of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton Method allows one to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient Method. The large-scale nature of FWI problems requires us, however, to carefully implement this Method to avoid prohibitive computational costs. First, this requires working in a matrix-free formalism and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be paid to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug--Toint Method, based on trust regions, and the Eisenstat and Walker stopping criterion, designed for a Method globalized by linesearch. We investigate the application of the truncated Newton Method to two test cases: The first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near-surface imaging problem for the reconstruction of high-velocity structures. In the latter case, we demonstrate that the presence of large amplitude multiscattered waves prevents standard Methods from converging while the truncated Newton Method provides more reliable results. Read More: http://epubs.siam.org/doi/abs/10.1137/120877854
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The truncated Newton Method for Full Waveform Inversion
2012Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) Methods use generally gradient based Method, such as the nonlinear conjugate gradient Method or more recently the l-BFGS quasi-Newton Method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these Methods inside a truncated Newton procedure. We demonstrate that the exact Newton Method can outperform the standard gradient-based Methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton Method.
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Optimization schemes for Full Waveform Inversion: the preconditioned truncated Newton Method
2012Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) Methods use generally gradient based Method, such as the nonlinear conjugate gradient Method or more recently the l-BFGS quasi-Newton Method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these Methods inside a truncated Newton procedure. We demonstrate that the exact Newton Method can outperform the standard gradient-based Methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton Method.
Stéphane Operto - One of the best experts on this subject based on the ideXlab platform.
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Full Waveform Inversion and the Truncated Newton Method
SIAM Review, 2017Co-Authors: Ludovic Métivier, Romain Brossier, Stéphane Operto, Jean VirieuxAbstract:Full waveform inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing the distance between predicted and recorded data. The predicted data are computed as the solution of a wave-propagation problem. Conventional numerical Methods for the solution of FWI problems are gradient-based Methods, such as the preconditioned steepest descent, the nonlinear conjugate gradient, or more recently the $l$-BFGS quasi-Newton algorithm. In this study, we investigate the desirability of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction, as it should help to mitigate finite-frequency effects and to better remove artifacts arising from multiscattered waves. For multiparameter reconstruction, the inverse Hessian operator also offers the possibility of better removing trade-offs due to coupling effects between parameter classes. The truncated Newton Method allows us to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through the conjugate gradient Method. The large-scale nature of FWI problems requires us, however, to carefully implement this Method to avoid prohibitive computational costs. First, this requires working in a matrix-free formalism and the capability of efficiently computing Hessian-vector products. For this purpose, we propose general second-order adjoint state formulas. Second, special attention must be paid to defining the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug--Toint Method, based on trust regions, and the Eisenstat and Walker stopping criterion, designed for a Method globalized by linesearch. We investigate the application of the truncated Newton Method to two case studies. The first is a standard case study in seismic imaging based on the Marmousi model. The second is inspired by a near-surface imaging problem for the reconstruction of high-velocity structures. In the latter case, we demonstrate that the presence of large amplitude multiscattered waves prevents standard Methods from converging, while the truncated Newton Method provides more reliable results.
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Full Waveform Inversion and the truncated Newton Method
SIAM Journal on Scientific Computing, 2013Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing a distance between predicted and recorded data. The predicted data is computed as the solution of a wave propagation problem. Conventional numerical Methods for the resolution of FWI problems are gradient-based Methods, such as the preconditioned steepest-descent, or more recently the l-BFGS quasi-Newton algorithm. In this study, we investigate the interest of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton Method allows one to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient Method. The large-scale nature of FWI problems requires however to carefully implement this Method to avoid prohibitive computational costs. First, this requires to work in a matrix-free formalism, and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be payed to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug-Toint Method, based on trust-regions, and the Eisenstat stopping criterion, designed for Method globalized by linesearch. We investigate the application of the truncated Newton Method to two test cases: the first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near-surface imaging problem for the reconstruction of high velocity structures. In the latter case, we demonstrate that the presence of large amplitude multi-scattered waves prevents standard Methods from converging while the truncated Newton Method provides more reliable results.
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Full Waveform Inversion and the Truncated Newton Method
SIAM Journal on Scientific Computing, 2013Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:ull waveform inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing the distance between predicted and recorded data. The predicted data are computed as the solution of a wave-propagation problem. Conventional numerical Methods for the resolution of FWI problems are gradient-based Methods, such as the preconditioned steepest descent, or more recently the $l$-BFGS quasi-Newton algorithm. In this study, we investigate the desirability of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton Method allows one to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient Method. The large-scale nature of FWI problems requires us, however, to carefully implement this Method to avoid prohibitive computational costs. First, this requires working in a matrix-free formalism and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be paid to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug--Toint Method, based on trust regions, and the Eisenstat and Walker stopping criterion, designed for a Method globalized by linesearch. We investigate the application of the truncated Newton Method to two test cases: The first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near-surface imaging problem for the reconstruction of high-velocity structures. In the latter case, we demonstrate that the presence of large amplitude multiscattered waves prevents standard Methods from converging while the truncated Newton Method provides more reliable results. Read More: http://epubs.siam.org/doi/abs/10.1137/120877854
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The truncated Newton Method for Full Waveform Inversion
2012Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) Methods use generally gradient based Method, such as the nonlinear conjugate gradient Method or more recently the l-BFGS quasi-Newton Method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these Methods inside a truncated Newton procedure. We demonstrate that the exact Newton Method can outperform the standard gradient-based Methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton Method.
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Optimization schemes for Full Waveform Inversion: the preconditioned truncated Newton Method
2012Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) Methods use generally gradient based Method, such as the nonlinear conjugate gradient Method or more recently the l-BFGS quasi-Newton Method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these Methods inside a truncated Newton procedure. We demonstrate that the exact Newton Method can outperform the standard gradient-based Methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton Method.
Ludovic Métivier - One of the best experts on this subject based on the ideXlab platform.
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Full Waveform Inversion and the Truncated Newton Method
SIAM Review, 2017Co-Authors: Ludovic Métivier, Romain Brossier, Stéphane Operto, Jean VirieuxAbstract:Full waveform inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing the distance between predicted and recorded data. The predicted data are computed as the solution of a wave-propagation problem. Conventional numerical Methods for the solution of FWI problems are gradient-based Methods, such as the preconditioned steepest descent, the nonlinear conjugate gradient, or more recently the $l$-BFGS quasi-Newton algorithm. In this study, we investigate the desirability of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction, as it should help to mitigate finite-frequency effects and to better remove artifacts arising from multiscattered waves. For multiparameter reconstruction, the inverse Hessian operator also offers the possibility of better removing trade-offs due to coupling effects between parameter classes. The truncated Newton Method allows us to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through the conjugate gradient Method. The large-scale nature of FWI problems requires us, however, to carefully implement this Method to avoid prohibitive computational costs. First, this requires working in a matrix-free formalism and the capability of efficiently computing Hessian-vector products. For this purpose, we propose general second-order adjoint state formulas. Second, special attention must be paid to defining the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug--Toint Method, based on trust regions, and the Eisenstat and Walker stopping criterion, designed for a Method globalized by linesearch. We investigate the application of the truncated Newton Method to two case studies. The first is a standard case study in seismic imaging based on the Marmousi model. The second is inspired by a near-surface imaging problem for the reconstruction of high-velocity structures. In the latter case, we demonstrate that the presence of large amplitude multiscattered waves prevents standard Methods from converging, while the truncated Newton Method provides more reliable results.
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Full Waveform Inversion and the truncated Newton Method
SIAM Journal on Scientific Computing, 2013Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing a distance between predicted and recorded data. The predicted data is computed as the solution of a wave propagation problem. Conventional numerical Methods for the resolution of FWI problems are gradient-based Methods, such as the preconditioned steepest-descent, or more recently the l-BFGS quasi-Newton algorithm. In this study, we investigate the interest of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton Method allows one to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient Method. The large-scale nature of FWI problems requires however to carefully implement this Method to avoid prohibitive computational costs. First, this requires to work in a matrix-free formalism, and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be payed to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug-Toint Method, based on trust-regions, and the Eisenstat stopping criterion, designed for Method globalized by linesearch. We investigate the application of the truncated Newton Method to two test cases: the first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near-surface imaging problem for the reconstruction of high velocity structures. In the latter case, we demonstrate that the presence of large amplitude multi-scattered waves prevents standard Methods from converging while the truncated Newton Method provides more reliable results.
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Full Waveform Inversion and the Truncated Newton Method
SIAM Journal on Scientific Computing, 2013Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:ull waveform inversion (FWI) is a powerful Method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This Method consists in minimizing the distance between predicted and recorded data. The predicted data are computed as the solution of a wave-propagation problem. Conventional numerical Methods for the resolution of FWI problems are gradient-based Methods, such as the preconditioned steepest descent, or more recently the $l$-BFGS quasi-Newton algorithm. In this study, we investigate the desirability of applying a truncated Newton Method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton Method allows one to better account for this operator. This Method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient Method. The large-scale nature of FWI problems requires us, however, to carefully implement this Method to avoid prohibitive computational costs. First, this requires working in a matrix-free formalism and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be paid to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug--Toint Method, based on trust regions, and the Eisenstat and Walker stopping criterion, designed for a Method globalized by linesearch. We investigate the application of the truncated Newton Method to two test cases: The first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near-surface imaging problem for the reconstruction of high-velocity structures. In the latter case, we demonstrate that the presence of large amplitude multiscattered waves prevents standard Methods from converging while the truncated Newton Method provides more reliable results. Read More: http://epubs.siam.org/doi/abs/10.1137/120877854
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The truncated Newton Method for Full Waveform Inversion
2012Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) Methods use generally gradient based Method, such as the nonlinear conjugate gradient Method or more recently the l-BFGS quasi-Newton Method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these Methods inside a truncated Newton procedure. We demonstrate that the exact Newton Method can outperform the standard gradient-based Methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton Method.
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Optimization schemes for Full Waveform Inversion: the preconditioned truncated Newton Method
2012Co-Authors: Ludovic Métivier, Romain Brossier, Jean Virieux, Stéphane OpertoAbstract:Full Waveform Inversion (FWI) Methods use generally gradient based Method, such as the nonlinear conjugate gradient Method or more recently the l-BFGS quasi-Newton Method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these Methods inside a truncated Newton procedure. We demonstrate that the exact Newton Method can outperform the standard gradient-based Methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton Method.
Orizon P. Ferreira - One of the best experts on this subject based on the ideXlab platform.
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A robust Kantorovich's theorem on the inexact Newton Method with relative residual error tolerance
Journal of Complexity, 2012Co-Authors: Orizon P. Ferreira, Benar Fux SvaiterAbstract:We prove that under semi-local assumptions, the inexact Newton Method with a fixed relative residual error tolerance converges Q-linearly to a zero of the nonlinear operator under consideration. Using this result we show that the Newton Method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on the Newton Method.
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A robust Kantorovich's theorem on inexact Newton Method with relative residual error tolerance
arXiv: Numerical Analysis, 2011Co-Authors: Orizon P. Ferreira, Benar Fux SvaiterAbstract:We prove that under semi-local assumptions, the inexact Newton Method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration. Using this result we show that Newton Method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on Newton Method.
