Journal ArticleDOI
Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation
Andreas Griewank,Andrea Walther +1 more
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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Checkmate: Breaking the Memory Wall with Optimal Tensor Rematerialization
Paras Jain,Ajay Jain,Aniruddha Nrusimha,Amir Gholami,Pieter Abbeel,Joseph E. Gonzalez,Kurt Keutzer,Ion Stoica +7 more
TL;DR: This work introduces Checkmate, a system that solves for optimal rematerialization schedules in reasonable times using off-the-shelf MILP solvers or near-optimal schedules with an approximation algorithm, then uses these schedules to accelerate millions of training iterations.
Journal ArticleDOI
Time-reversal checkpointing methods for RTM and FWI
TL;DR: The optimal trade-off between memory usage and recomputation can be further improved under the assumption that the information needed to do temporal crosscorrelation is smaller than the information required to restart a simulation from a given time step.
Journal ArticleDOI
Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization
TL;DR: Kadam et al. as mentioned in this paper proposed a method for solving dynamic optimization problems based on neighboring-extremal updates suitable for applications in nonlinear model-predictive control and dynamic real-time optimization.
Patent
Iterative inversion of data from simultaneous geophysical sources
Jerome R. Krebs,John E. Anderson,Ramesh Neelamani,Charlie Jing,David L. Hinkley,Thomas A. Dickens,Christine E. Krohn,Peter Traynin +7 more
TL;DR: In this article, a method for reducing the time needed to perform geophysical inversion by using simultaneous encoded sources in the simulation steps of the inversion process is presented, where the geophysical survey data are prepared by encoding (3) a group of source gathers, using for each gather a different encoding signature selected from a set of non- equivalent encoding signatures.
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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