Journal ArticleDOI
Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation
Andreas Griewank,Andrea Walther +1 more
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TLDR
This article presents the function revolve, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion and is intended to be used as an explicit “controller” for running a time-dependent applications program.Abstract:
In its basic form, the reverse mode of computational differentiation yields the gradient of a scalar-valued function at a cost that is a small multiple of the computational work needed to evaluate the function itself. However, the corresponding memory requirement is proportional to the run-time of the evaluation program. Therefore, the practical applicability of the reverse mode in its original formulation is limited despite the availability of ever larger memory systems. This observation leads to the development of checkpointing schedules to reduce the storage requirements. This article presents the function revolve, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion. This routine is intended to be used as an explicit “controller” for running a time-dependent applications program.read more
Citations
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Journal ArticleDOI
An optimal memory‐reduced procedure for calculating adjoints of the instationary Navier‐Stokes equations
TL;DR: In this paper, the storage problem arising in the numerical calculation of the appearing adjoint equations is tackled by proposing a low-storage approach which utilizes optimal checkpointing, which allows a remarkable memory reduction by accepting a slight increase in run-time caused by repeated forward integrations.
Patent
Artifact reduction in iterative inversion of geophysical data
TL;DR: In this paper, a method for reducing artifacts in a subsurface physical properties model (120) inferred by iterative inversion (140) of geophysical data (130), wherein the artifacts are associated with some approximation (110) made during the iteration, is presented.
Journal ArticleDOI
Wavefield reconstruction by interpolating significantly decimated boundaries
TL;DR: In this paper, the authors proposed three methods: read the stored forward wavefield from the disk, using the final snapshot and the stored boundaries via reverse propagation, and remodeling using checkpointing from stored state to another state.
Patent
Methods for Approximating Hessian Times Vector Operation in Full Wavefield Inversion
Sunwoong Lee,Anatoly Baumstein +1 more
TL;DR: In this paper, the Hessian of the objective function, times a vector, is estimated in order to compute an update in an iterative optimization solution to a partial differential equation such as the wave equation, used for example in full wave field inversion of seismic data.
Book ChapterDOI
Advantages of Binomial Checkpointing for Memory-reduced Adjoint Calculations
Andrea Walther,Andreas Griewank +1 more
TL;DR: The more common multi-level checkpointing as well as the less known binomial checkpointing are presented and the checkpointing approaches are compared with respect to the number of time steps the adjoint of which can be calculated, the run-time needed for the adjointed calculation and the memory requirement.
References
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Book
Numerical methods for conservation laws
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
Book
Optimal Control of Systems Governed by Partial Differential Equations
TL;DR: In this paper, the authors consider the problem of minimizing the sum of a differentiable and non-differentiable function in the context of a system governed by a Dirichlet problem.
Book
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Andreas Griewank,Andrea Walther +1 more
TL;DR: This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity.
Journal ArticleDOI
Upwind difference schemes for hyperbolic systems of conservation laws
Stanley Osher,Fred Solomon +1 more
TL;DR: In this article, a new upwind finite difference approximation to systems of nonlinear hyperbolic conservation laws has been derived. But the scheme has desirable properties for shock calculations, such as unique and sharp shocks.
Journal ArticleDOI
Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation
TL;DR: It is shown here that, by a recursive scheme related to the multilevel differentiation approach of Volin and Ostrovskii, the growth in both temporal and spatial complexity can be limited to a fixed multiple of log(T).
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Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
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