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
More filters
Book ChapterDOI
Storing Versus Recomputation on Multiple DAGs
TL;DR: A heuristic approach for exploiting finer granularity recomputations to reduce the storage requirements and thereby improve the overall adjoint efficiency without the need for manual intervention is considered.
Topology optimization and lattice Boltzmann methods
TL;DR: It is demonstrated that topology optimization can account for unsteady flow effects during the optimization process, and it is found that the weakly compressible nature of the lattice Boltzmann method leads to a discrepancy in the predicted outcomes.
Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations
Archis Joglekar,Alexander Thomas +1 more
TL;DR: This work creates a differentiable solver for the 3D partial-differential-equation describing the plasma kinetics and introduces a domain-specific objective function, and performs gradient-based optimization of neural networks that provide forcing function parameters to the differentiablesolver given a set of initial conditions.
DissertationDOI
Adjoint based analysis for swirling and reacting flows
TL;DR: In this article, the use of adjoints in a reacting and swirling flow setting is discussed, and an algorithmic technique is developed to facilitate the use for the complicated governing equations that arise from reacting flow.
Proceedings ArticleDOI
Enabling wave-based inversion on GPUs with randomized trace estimation
TL;DR: These findings open the enticing perspective of 3D wave-based inversion technology with a memory footprint that matches the hardware and that runs exclusively on clusters of GPUs without the undesirable need to offload certain tasks to CPUs.
References
More filters
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).
Related Papers (5)
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Andreas Griewank,Andrea Walther +1 more
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, Second Edition
Andreas Griewank,Andrea Walther +1 more