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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Journal ArticleDOI
An adjoint method for control of liquid-gas flows using a sharp interface model
TL;DR: In this paper , a computational, continuous adjoint framework for the control of liquid-gas flows using a sharp interface model is presented, where the two-phase Navier-Stokes equations are solved using a mass-conserving geometric volume-of-fluid method, while the adjoint equations consider a level set-based representation of the interface.
Orthogonal bases for polynomial regres- sion with derivative information in uncer- tainty quantification
TL;DR: In this paper, the authors discuss the choice of polynomial basis for approximation of uncertainty propagation through complex simulation models with capability to output derivative information, and demonstrate the benefits of the basis in the propagation of material uncertainties through a simplified model of heat transport in a nuclear reactor core.
Journal ArticleDOI
An adjoint method for control of liquid-gas flows using a sharp interface model
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TL;DR: In this paper, a fine-grained interactive language-image pre-training (FILIP) is proposed to achieve finer-level alignment through a cross-modal late interaction mechanism, which uses a token-wise maximum similarity between visual and textual tokens to guide the contrastive objective.
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TL;DR: In this paper, the authors proposed a new imaging condition which construction is inspired from with some approximations required to keep admissible computational costs, which is the so-called optimal checkpointing.
References
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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
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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.
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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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