The Experts below are selected from a list of 99 Experts worldwide ranked by ideXlab platform
Omar Ghattas - One of the best experts on this subject based on the ideXlab platform.
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An inexact Gauss–Newton method for Inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model
2016Co-Authors: Omar GhattasAbstract:ABSTRACT. We propose an infinite-dimensional adjoint-based inexact Gauss–Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the Number of Stokes solutions required to solve the inverse problem is insensitive to the Number of Inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the Inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations. 1
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an inexact gauss newton method for Inversion of basal sliding and rheology parameters in a nonlinear stokes ice sheet model
Journal of Glaciology, 2012Co-Authors: Noemi Petra, Hongyu Zhu, Georg Stadler, Thomas J R Hughes, Omar GhattasAbstract:We propose an infinite-dimensional adjoint-based inexact Gauss―Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the Number of Stokes solutions required to solve the inverse problem is insensitive to the Number of Inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the Inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.
Bernd J Wintersperger - One of the best experts on this subject based on the ideXlab platform.
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Inversion group ig fitting a new t1 mapping method for modified look locker Inversion recovery molli that allows arbitrary Inversion groupings and rest periods including no rest period
Magnetic Resonance in Medicine, 2016Co-Authors: Marshall S Sussman, Issac Y Yang, Bernd J WinterspergerAbstract:Purpose The Modified Look-Locker Inversion Recovery (MOLLI) technique is used for T1 mapping in the heart. However, a drawback of this technique is that it requires lengthy rest periods in between Inversion groupings to allow for complete magnetization recovery. In this work, a new MOLLI fitting algorithm (Inversion group [IG] fitting) is presented that allows for arbitrary combinations of Inversion groupings and rest periods (including no rest period). Theory and Methods Conventional MOLLI algorithms use a three parameter fitting model. In IG fitting, the Number of parameters is two plus the Number of Inversion groupings. This increased Number of parameters permits any Inversion grouping/rest period combination. Validation was performed through simulation, phantom, and in vivo experiments. Results IG fitting provided T1 values with less than 1% discrepancy across a range of Inversion grouping/rest period combinations. By comparison, conventional three parameter fits exhibited up to 30% discrepancy for some combinations. The one drawback with IG fitting was a loss of precision—approximately 30% worse than the three parameter fits. Conclusion IG fitting permits arbitrary Inversion grouping/rest period combinations (including no rest period). The cost of the algorithm is a loss of precision relative to conventional three parameter fits. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.
Noemi Petra - One of the best experts on this subject based on the ideXlab platform.
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an inexact gauss newton method for Inversion of basal sliding and rheology parameters in a nonlinear stokes ice sheet model
Journal of Glaciology, 2012Co-Authors: Noemi Petra, Hongyu Zhu, Georg Stadler, Thomas J R Hughes, Omar GhattasAbstract:We propose an infinite-dimensional adjoint-based inexact Gauss―Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the Number of Stokes solutions required to solve the inverse problem is insensitive to the Number of Inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the Inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.
Thomas J R Hughes - One of the best experts on this subject based on the ideXlab platform.
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an inexact gauss newton method for Inversion of basal sliding and rheology parameters in a nonlinear stokes ice sheet model
Journal of Glaciology, 2012Co-Authors: Noemi Petra, Hongyu Zhu, Georg Stadler, Thomas J R Hughes, Omar GhattasAbstract:We propose an infinite-dimensional adjoint-based inexact Gauss―Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the Number of Stokes solutions required to solve the inverse problem is insensitive to the Number of Inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the Inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.
Hongyu Zhu - One of the best experts on this subject based on the ideXlab platform.
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an inexact gauss newton method for Inversion of basal sliding and rheology parameters in a nonlinear stokes ice sheet model
Journal of Glaciology, 2012Co-Authors: Noemi Petra, Hongyu Zhu, Georg Stadler, Thomas J R Hughes, Omar GhattasAbstract:We propose an infinite-dimensional adjoint-based inexact Gauss―Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the Number of Stokes solutions required to solve the inverse problem is insensitive to the Number of Inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the Inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.
