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    188宝金博页面版: Making Automatic Differentiation Truly Automatic： Coupling PETSc with ADIC

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    内容提示： Making Automatic Dif f erentiation TrulyAutomatic: Coupling PETSc with ADICPaul Hovland, Boyana Norris, and Barry SmithMathematics and Computer Science DivisionArgonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA{hovland, norris, bsmith}@mcs.anl.govhttp://www.mcs.anl.govAbstract. Despite its name, automatic dif f erentiation (AD) is often farfrom an automatic process. Often one must specify independent and de-pendent variables, indicate the derivative quantities to be computed, andperha...

    文档格式：PDF | 页数：10 | 浏览次数：204 | 上传日期：2018-03-30 07:39:07 | 文档星级：
    Making Automatic Dif f erentiation TrulyAutomatic: Coupling PETSc with ADICPaul Hovland, Boyana Norris, and Barry SmithMathematics and Computer Science DivisionArgonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA{hovland, norris, bsmith}@mcs.anl.govhttp://www.mcs.anl.govAbstract. Despite its name, automatic dif f erentiation (AD) is often farfrom an automatic process. Often one must specify independent and de-pendent variables, indicate the derivative quantities to be computed, andperhaps even provide information about the structure of the Jacobiansor Hessians being computed. However, when AD is used in conjunctionwith a toolkit with well-def i ned interfaces, many of these issues do notarise. We describe recent research into coupling the ADIC automatic dif-ferentiation tool with PETSc, a toolkit for the parallel numerical solutionof PDEs. This research leverages the interfaces and objects of PETSc tomake the AD process very nearly transparent.1 IntroductionMany varieties of scientif i c computation, including the numerical solution ofnonlinear partial dif f erential equations (PDEs), require derivatives. For compli-cated functions, it can be a dif f i cult task to implement derivative computationsby hand. In contrast, f i nite dif f erence approximations are simple to implement,but they suf f er from both roundof f and truncation error. Furthermore, f i ndinga stepsize that balances these sources of error (thus minimizing the total error)can be dif f i cult. Automatic dif f erentiation (AD) [1,2] of f ers an alternative thatminimizes human ef f ort and eliminates truncation error. For this reason, auto-matic dif f erentiation has become a popular tool for scientif i c computing (see, forexample [3,4]).One obstacle to widespread adoption of automatic dif f erentiation is that theprocess is often far from automatic. To achieve acceptable levels of performance,the user may need to specify independent and dependent variables, indicatethe derivatives to be computed, and provide information about the structureof the Jacobians or Hessians being computed. Previous work [5–7], however,has demonstrated that when AD is used in conjunction with a toolkit withwell-def i ned interfaces, many of these issues do not arise. This paper describesresearch into coupling the ADIC [8] automatic dif f erentiation tool with PETSc,a toolkit for the parallel numerical solution of PDEs [9]. This research extendsearlier results by directly exploiting the sparsity structure of the Jacobians tobe computed. It also provides a strategy for computing Jacobians in parallel,P.M.A. Sloot et al. (Eds.): ICCS 2002, LNCS 2330, pp. 1087−1096, 2002.? Springer-Verlag Berlin Heidelberg 2002

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