Publication: Parallelizable adjoint stencil computations using transposed forward-mode algorithmic differentiation
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Parallelizable adjoint stencil computations using transposed forward-mode algorithmic differentiation

- Article in a journal -
 

Area
Computational Fluid Dynamics

Author(s)
Jan C. Hückelheim , Paul D. Hovland , Michelle M. Strout , Jens-Dominik Müller

Published in
Special issue of Optimization Methods & Software: Advances in Algorithmic Differentiation Optimization Methods & Software

Editor(s)
Bruce Christianson, Shaun A. Forth, Andreas Griewank, Paul D. Hovland

Year
2018

Publisher
Taylor & Francis

Abstract
Algorithmic differentiation (ad) is a tool for generating discrete adjoint solvers, which efficiently compute gradients of functions with many inputs, for example for use in gradient-based optimization. ad is often applied to large computations such as stencil operators, which are an important part of most structured-mesh PDE solvers. Stencil computations are often parallelized, for example by using OpenMP, and optimized by using techniques such as cache-blocking and tiling to fully utilize multicore CPUs and many-core accelerators and GPUs. Differentiating these codes with conventional reverse-mode ad results in adjoint codes that cannot be expressed as stencil operations and may not be easily parallelizable. They thus leave most of the compute power of modern architectures unused. We present a method that combines forward-mode ad and loop transformation to generate adjoint solvers that use the same memory access pattern as the original computation that they are derived from and can benefit from the same optimization techniques. The effectiveness of this method is demonstrated by generating a scalable adjoint CFD solver for multicore CPUs and Xeon Phi accelerators.

Cross-References
Christianson2018Sio

AD Tools
TAPENADE

AD Theory and Techniques
Adjoint, Code Optimization, control-flow reversal, Data Flow Analysis, data-flow reversal, Implementation Strategies, Parallelism, Performance, Reverse Mode, Source transformation

BibTeX
@ARTICLE{
         Huckelheim2018Pas,
       crossref = "Christianson2018Sio",
       author = "Jan C. H{\"u}ckelheim and Paul D. Hovland and Michelle M. Strout and
         Jens-Dominik M{\"u}ller",
       title = "Parallelizable adjoint stencil computations using transposed forward-mode algorithmic
         differentiation",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "672--693",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2018.1435654",
       url = "https://www.tandfonline.com/doi/abs/10.1080/10556788.2018.1435654",
       eprint = "https://www.tandfonline.com/doi/pdf/10.1080/10556788.2018.1435654",
       abstract = "Algorithmic differentiation (AD) is a tool for generating discrete adjoint solvers,
         which efficiently compute gradients of functions with many inputs, for example for use in
         gradient-based optimization. AD is often applied to large computations such as stencil operators,
         which are an important part of most structured-mesh PDE solvers. Stencil computations are often
         parallelized, for example by using OpenMP, and optimized by using techniques such as cache-blocking
         and tiling to fully utilize multicore CPUs and many-core accelerators and GPUs. Differentiating
         these codes with conventional reverse-mode AD results in adjoint codes that cannot be expressed as
         stencil operations and may not be easily parallelizable. They thus leave most of the compute power
         of modern architectures unused. We present a method that combines forward-mode AD and loop
         transformation to generate adjoint solvers that use the same memory access pattern as the original
         computation that they are derived from and can benefit from the same optimization techniques. The
         effectiveness of this method is demonstrated by generating a scalable adjoint CFD solver for
         multicore CPUs and Xeon Phi accelerators.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank and Paul D. Hovland",
       ad_area = "Computational Fluid Dynamics",
       ad_tools = "TAPENADE",
       ad_theotech = "Adjoint, Code Optimization, control-flow reversal, Data Flow Analysis, data-flow
         reversal, Implementation Strategies, Parallelism, Performance, Reverse Mode, Source
         transformation"
}


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