Reverse Automatic Differentiation for Optimum Design: From Adjoint State Assembly to Gradient Computation

Courty, Francois; Dervieux, Alain; Koobus, Bruno; Hascoët, Laurent

doi:10.1080/10556780310001610501

Cited by 29 publications

(20 citation statements)

References 6 publications

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“…Starting from an existing source code which numerically solves the state pde's to compute the scalar or vector objective function value(s), an automatic differentiation software, [29,30], generates a new code which additionally computes the δF δb i values, according to a set of linguistic and mathematical rules. On condition that the analysis software is available as source code, the development cost of the optimization method through automatic differentiation becomes negligible, despite the high memory requirements, [31].…”

Section: Automatic Differentiationmentioning

confidence: 99%

Aerodynamic Shape Optimization Using First and Second Order Adjoint and Direct Approaches

Papadimitriou

Giannakoglou

2008

Arch Computat Methods Eng

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This paper focuses on discrete and continuous adjoint approaches and direct differentiation methods that can efficiently be used in aerodynamic shape optimization problems. The advantage of the adjoint approach is the computation of the gradient of the objective function at cost which does not depend upon the number of design variables. An extra advantage of the formulation presented below, for the computation of either first or second order sensitivities, is that the resulting sensitivity expressions are free of field integrals even if the objective function is a field integral. This is demonstrated using three possible objective functions for use in internal aerodynamic problems; the first objective is for inverse design problems where a target pressure distribution along the solid walls must be reproduced; the other two quantify viscous losses in duct or cascade flows, cast as either the reduction in total pressure between the inlet and outlet or the field integral of entropy generation. From the mathematical point of view, the three functions are defined over different parts of the domain or its boundaries, and this strongly affects the adjoint formulation. In the second part of this paper, the same discrete and continuous adjoint formulations are combined with direct differentiation methods to compute the Hessian matrix of the objective function. Although the direct differentiation for the computation of the gradient is time consuming, it may support the adjoint method to calculate the exact Hessian matrix components with the minimum CPU cost. Since, however, the CPU cost is proportional to the number of design variables, a well performing optimization scheme, based on the exactly computed Hessian during the starting cycle and a quasi Newton (BFGS) scheme during the next cycles, is proposed.

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Section: Automatic Differentiationmentioning

confidence: 99%

Aerodynamic Shape Optimization Using First and Second Order Adjoint and Direct Approaches

Papadimitriou

Giannakoglou

2008

Arch Computat Methods Eng

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“…The source-transformation approach differentiates a function by parsing the code, performing various analyzes and writing a set of source files with new definitions to implement AD expressions. While the source transformation approach has been very successful and well implemented for languages such as Fortran 77/90 [Bischof et al 1992;Faure 2005;Hascoet 2004;Courty et al 2003], as of the time of this writing, there are no such tools for differentiating ANSI/ISO C++. Therefore, we will not consider source transformation tools any further in this article.…”

Section: Introductionmentioning

confidence: 99%

“…The general process consists of decomposing the function into elemental steps, applying simple derivative rules to individual operations and then using the chain rule to provide a final derivative calculation of the overall function. The reverse mode of automatic differentiation was introduced by Linnainmaa [1976] and later further exploited by Speelpenning [1980] and Courty et al [2003]. Our efforts have focused on the forward mode of AD and therefore we do not consider reverse mode AD any further here.…”

Section: Introductionmentioning

confidence: 99%

Hybrid differentiation strategies for simulation and analysis of applications in C++

Bartlett

Waanders

Berggren

2008

ACM Trans. Math. Softw.

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Computationally efficient and accurate derivatives are important to the success of many different types of numerical methods. Automatic differentation (AD) approaches compute truncation-free derivatives and can be efficient in many cases. Although present AD tools can provide a convenient implementation mechanism, the computational efficiency rarely compares to analytically derived versions that have been carefully implemented. The focus of this work is to combine the strength of these methods into a hybrid strategy that attempts to achieve an optimal balance of implementation and computational efficiency by selecting the appropriate components of the target algorithms for AD and analytical derivation. Although several AD approaches can be considered, our focus is on the use of template overloading forward AD tools in C++ applications. We demonstrate this hybrid strategy for a system of partial differential equations in gas dynamics. These methods apply however to other systems of differentiable equations, including DAEs and ODEs.

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“…with reasonable CPU time). They are often supported by tools that compute the derivatives of the objective function; such as the adjoint techniques [9,10], the Automatic Diffrentiation (AD) [11,12], the surrogate models (Radial Basis Function(RBF), Artificial Neural Networks (ANN), etc.) [13].…”

Section: Introductionmentioning

confidence: 99%

Hessian transfer for multilevel and adaptive shape optimization

Majd¹,

Ouchetto²,

Désidéri³

et al. 2017

Int. J. Simul. Multisci. Des. Optim.

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-We have developed a multilevel and adaption parametric strategies solved by optimization algorithms which require only the availability of objective function values but no derivative information. The key success of these hierarchical strategies refer to the quality of the downward and upward transfers of information. In this paper, we extend our approach when using a derivative-based optimization algorithms. The aim is to better re-initialize the Hessian and the gradient during the optimization process based on our construction of the downward and upward operators. The efficiency of this proposed approach is demonstrated by numerical experiments on an inverse shape model.

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Reverse Automatic Differentiation for Optimum Design: From Adjoint State Assembly to Gradient Computation

Cited by 29 publications

References 6 publications

Aerodynamic Shape Optimization Using First and Second Order Adjoint and Direct Approaches

Aerodynamic Shape Optimization Using First and Second Order Adjoint and Direct Approaches

Hybrid differentiation strategies for simulation and analysis of applications in C++

Hessian transfer for multilevel and adaptive shape optimization

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