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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MonographDOI
Subduction in an Eddy-Resolving State Estimate of the Northeast Atlantic Ocean
TL;DR: In this article, a regional, eddy-resolving numerical model is combined with observations to produce a state estimate of the ocean circulation. But the model is only weakly nonlinear in the eastern region of the subtropical gyre and no fundamental obstacle exists to constrain the model to both the large scale circulation and the eddy scale.
Journal ArticleDOI
Designing self-assembling kinetics with differentiable statistical physics models.
TL;DR: In this paper, the inverse problem of designing component interactions to target emergent structure is addressed, which is fundamental to numerous applications in biotechnology, materials science, and statistical physics.
Proceedings ArticleDOI
Reverse-mode automatic differentiation and optimization of GPU kernels via enzyme
William S. Moses,Valentin Churavy,Ludger Paehler,Jan Hückelheim,Sri Hari Krishna Narayanan,Michel Schanen,Johannes Doerfert +6 more
TL;DR: Enzyme as discussed by the authors is a LLVM compiler plugin that performs reverse-mode automatic differentiation (AD) and thus generates high performance gradients of programs in languages including C/C++, Fortran, Julia, and Rust.
Journal ArticleDOI
Adjoint Complement to the Volume-of-Fluid Method for Immiscible Flows
TL;DR: The paper analyses the primal and adjoint equations for an engineering model problem and refers to a shape-optimization of a generic 3D underwater vehicle and underlines a negligible influence of the free mobility parameter.
Posted Content
Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method
TL;DR: The results show that a straightforward discretization of the continuous gradient differs from the discretely exact gradient, and thus is not consistent with the discretized objective, which may cause difficulties in the convergence of gradient based algorithms for solving optimization problems.
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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