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Eric Rignot - One of the best experts on this subject based on the ideXlab platform.
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inversion of basal friction in antarctica using exact and incomplete Adjoints of a higher order model
Journal of Geophysical Research, 2013Co-Authors: Mathieu Morlighem, Eric Larour, Helene Seroussi, Eric RignotAbstract:Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete Adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.
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inversion of basal friction in antarctica using exact and incomplete Adjoints of a higher order model
Journal of Geophysical Research, 2013Co-Authors: Mathieu Morlighem, Eric Larour, Helene Seroussi, Eric RignotAbstract:Author(s): Morlighem, M; Seroussi, H; Larour, E; Rignot, E | Abstract: Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete Adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.
Adrian Sandu - One of the best experts on this subject based on the ideXlab platform.
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space time adaptive solution of inverse problems with the discrete adjoint method
Journal of Computational Physics, 2014Co-Authors: Mihai Alexe, Adrian SanduAbstract:This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete Adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space–time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge–Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space–time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.
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continuous versus discrete advection Adjoints in chemical data assimilation with cmaq
Atmospheric Environment, 2011Co-Authors: Tianyi Gou, Adrian SanduAbstract:Abstract Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. In the four dimensional variational (4D-Var) framework data assimilation is formulated as an optimization problem, which is solved using gradient based optimization methods. The 4D-Var gradient is obtained by forcing the adjoint model with observation increments. The construction of the adjoint model requires considerable development effort. In the continuous approach the adjoint differential equations are discretized. In the discrete approach the numerical solution of the forward equations is differentiated. The two routes lead to different gradients. In this paper we investigate numerically the effect of using discrete and continuous Adjoints of the advection equation in chemical transport modeling. Continuous advection Adjoints are easily implemented by calling the same advection subroutines as the forward model, with a sign change for the winds, and with rescaling the solution. Discrete advection Adjoints involve the differentiation of a nonlinear, monotonic advection scheme like the piecewise parabolic method. The numerical experiments are carried out with CMAQ-ADJ. The results show that, while discrete advection Adjoints are more accurate in point-to-point comparisons against finite differences, the continuous Adjoints of advection perform better as gradients for optimization in 4D-Var data assimilation.
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discrete second order Adjoints in atmospheric chemical transport modeling
Journal of Computational Physics, 2008Co-Authors: Adrian Sandu, Lin ZhangAbstract:Atmospheric chemical transport models (CTMs) are essential tools for the study of air pollution, for environmental policy decisions, for the interpretation of observational data, and for producing air quality forecasts. Many air quality studies require sensitivity analyses, i.e., the computation of derivatives of the model output with respect to model parameters. The derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis. While the traditional (first order) adjoint models give the gradient of the cost functional with respect to parameters, second order adjoint models give second derivative information in the form of products between the Hessian of the cost functional and a vector (representing a perturbation in sensitivity analysis, a search direction in optimization, an eigenvector, etc.). In this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three-dimensional atmospheric CTMs. The tools include discrete second order Adjoints of Runge-Kutta and of Rosenbrock time stepping methods for stiff equations together with efficient implementation strategies. Numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis, optimization, uncertainty quantification and the calculation of directions of maximal error growth in three-dimensional atmospheric CTMs.
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on the properties of runge kutta discrete Adjoints
International Conference on Computational Science, 2006Co-Authors: Adrian SanduAbstract:In this paper we analyze the consistency and stability properties of Runge-Kutta discrete Adjoints. Discrete Adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis uses the concept of elementary differentials and reveals that the discrete Runge-Kutta adjoint method has the same order of accuracy as the original, forward method. A singular perturbation analysis reveals that discrete Adjoints of stiff Runge-Kutta methods are well suited for stiff problems.
Mathieu Morlighem - One of the best experts on this subject based on the ideXlab platform.
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an approach to computing discrete Adjoints for mpi parallelized models applied to ice sheet system model 4 11
Geoscientific Model Development, 2016Co-Authors: Eric Larour, Jean Utke, Anton Bovin, Mathieu Morlighem, Gilberto PerezAbstract:Abstract. Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of Adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM. We present a comprehensive approach to (1) carry out type changing through the ISSM, hence facilitating operator overloading, (2) bind to external solvers such as MUMPS and GSL-LU, and (3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica.
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inversion of basal friction in antarctica using exact and incomplete Adjoints of a higher order model
Journal of Geophysical Research, 2013Co-Authors: Mathieu Morlighem, Eric Larour, Helene Seroussi, Eric RignotAbstract:Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete Adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.
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inversion of basal friction in antarctica using exact and incomplete Adjoints of a higher order model
Journal of Geophysical Research, 2013Co-Authors: Mathieu Morlighem, Eric Larour, Helene Seroussi, Eric RignotAbstract:Author(s): Morlighem, M; Seroussi, H; Larour, E; Rignot, E | Abstract: Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete Adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.
Juan J Alonso - One of the best experts on this subject based on the ideXlab platform.
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coupled adjoint based sensitivities in large displacement fluid structure interaction using algorithmic differentiation
International Journal for Numerical Methods in Engineering, 2018Co-Authors: Ruben Sanchez, Tim Albring, Rafael Palacios, Nicolas R Gauger, Thomas D Economon, Juan J AlonsoAbstract:Summary A methodology for the calculation of gradients with respect to design parameters in general Fluid-Structure Interaction problems is presented. It is based on fixed-point iterations on the adjoint variables of the coupled system using Algorithmic Differentiation. This removes the need for the construction of the analytic Jacobian for the coupled physical problem, which is the usual limitation for the computation of Adjoints in most realistic applications. The formulation is shown to be amenable to partitioned solution methods for the adjoint equations. It also poses no restrictions to the nonlinear physics in either the fluid or structural field, other than the existence of a converged solution to the primal problem from which to compute the Adjoints. We demonstrate the applicability of this procedure and the accuracy of the computed gradients on coupled problems involving viscous flows with geometrical and material non-linearities in the structural domain. This article is protected by copyright. All rights reserved.
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error estimation for high speed flows using continuous and discrete Adjoints
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010Co-Authors: Karthikeyan Duraisamy, Juan J Alonso, Francisco Palacios, Praveen ChandrashekarAbstract:In this work, the utility of the adjoint equations in error estimation of functional outputs and goal-oriented mesh adaptation is investigated with specific emphasis towards application to high speed flows with strong shocks. Continuous and discrete adjoint formulations are developed for the compressible Euler equations and the accuracy and robustness of the implementation is assessed by evaluating adjoint-computed sensitivities. The two-grid approach of Venditti and Darmofal 1 - where the flow and adjoint solutions on a baseline mesh are processed to estimate the functional on a finer mesh - is used for error estimation and mesh adaptation. Using a carefully designed set of test cases for the quasi one dimensional Euler equations, it is shown that discrete Adjoints can be used to estimate the fine grid functional more accurately, whereas continuous Adjoints are marginally better at estimating the analytical value of the functional when the flow and adjoint solutions are well resolved. These observations appear to be true in multi-dimensional inviscid flows, but the distinction is not as clear. The discrete adjoint is shown to be robust when applied to goal oriented mesh adaptation in a flow with multiple shocks, and hence offers promise as a viable strategy to control the numerical error in Hypersonic flow applications.
Eric Larour - One of the best experts on this subject based on the ideXlab platform.
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an approach to computing discrete Adjoints for mpi parallelized models applied to ice sheet system model 4 11
Geoscientific Model Development, 2016Co-Authors: Eric Larour, Jean Utke, Anton Bovin, Mathieu Morlighem, Gilberto PerezAbstract:Abstract. Within the framework of sea-level rise projections, there is a strong need for hindcast validation of the evolution of polar ice sheets in a way that tightly matches observational records (from radar, gravity, and altimetry observations mainly). However, the computational requirements for making hindcast reconstructions possible are severe and rely mainly on the evaluation of the adjoint state of transient ice-flow models. Here, we look at the computation of Adjoints in the context of the NASA/JPL/UCI Ice Sheet System Model (ISSM), written in C++ and designed for parallel execution with MPI. We present the adaptations required in the way the software is designed and written, but also generic adaptations in the tools facilitating the adjoint computations. We concentrate on the use of operator overloading coupled with the AdjoinableMPI library to achieve the adjoint computation of the ISSM. We present a comprehensive approach to (1) carry out type changing through the ISSM, hence facilitating operator overloading, (2) bind to external solvers such as MUMPS and GSL-LU, and (3) handle MPI-based parallelism to scale the capability. We demonstrate the success of the approach by computing sensitivities of hindcast metrics such as the misfit to observed records of surface altimetry on the northeastern Greenland Ice Stream, or the misfit to observed records of surface velocities on Upernavik Glacier, central West Greenland. We also provide metrics for the scalability of the approach, and the expected performance. This approach has the potential to enable a new generation of hindcast-validated projections that make full use of the wealth of datasets currently being collected, or already collected, in Greenland and Antarctica.
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inversion of basal friction in antarctica using exact and incomplete Adjoints of a higher order model
Journal of Geophysical Research, 2013Co-Authors: Mathieu Morlighem, Eric Larour, Helene Seroussi, Eric RignotAbstract:Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete Adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.
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inversion of basal friction in antarctica using exact and incomplete Adjoints of a higher order model
Journal of Geophysical Research, 2013Co-Authors: Mathieu Morlighem, Eric Larour, Helene Seroussi, Eric RignotAbstract:Author(s): Morlighem, M; Seroussi, H; Larour, E; Rignot, E | Abstract: Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete Adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.