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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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
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Posted Content
Optimal Checkpointing for Adjoint Multistage Time-Stepping Schemes.
TL;DR: In this paper, the authors proposed two checkpointing strategies that minimize the number of recomputations needed when performing discrete adjoint computations using multistage time-stepping schemes, which requires computing several substeps within one complete time step.
Journal ArticleDOI
Monochromatic wave equation traveltime inversion in vertical transverse isotropic media: Theory and application
TL;DR: In this paper , a frequency-domain anisotropic wave equation traveltime inversion (WTI) method using only monochromatic wavefields during inversion is proposed.
Journal ArticleDOI
On syntax-directed adjoint fortran code
Uwe Naumann,Jan Riehme +1 more
TL;DR: An L-attributed grammar is presented for the single-pass generation of intraprocedural adjoint code for a subset of Fortran to integrate the syntax directed approach into the front-end of the NAGWare Fortran compiler.
Proceedings ArticleDOI
A modular software framework supporting simulation-driven optimization techniques
TL;DR: This paper introduces the “Time-Stepping for Optimization” software framework — or TSOpt — to aid solution of SDO problems, and demonstrates the effect of low-fidelity wind data for a trajectory-based optimization problem in MATLAB.
Posted ContentDOI
Optimization of the WRFV3.7 adjoint model
TL;DR: In this article, the authors focused on a new strategy for productively improving the performance of adjoint models by using several techniques including the push/pop-free method, careful Input/Output (IO) analysis and the use of the conception of the adjoint locality.
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.
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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.
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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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