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A Case Study in Adjoint Sensitivity Analysis of Parameter Calibration

Procedia Computer Science 2016年 80卷 201-211页

作者： Johannes Lotz Marc Schwalbach Uwe Naumann LuFG Informatik 12: Software and Tools for Computational Engineering RWTH Aachen Germany Von Karman Institute for Fluid Dynamics Belgium

Adjoint sensitivity computation of parameter estimation problems is a widely used technique in the field of computational science and engineering for retrieving derivatives of a cost functional with respect to parameters efficiently. Those derivatives can be used, e.g. for sensitivity analysis, optimization, or robustness analysis. Deriving and implementing adjoint code is an error-prone, non-trivial task which can be avoided by using Algorithmic Differentiation (AD) software. Generating adjoint code by AD software has the downside of usually requiring a huge amount of memory as well as a non-optimal run time. In this article, we couple two approaches for achieving both, a robust and efficient adjoint code: symbolically derived adjoint formulations and AD. Comparisons are carried out for a real-world case study originating from the remote atmospheric sensing simulation software JURASSIC developed at the Institute of Energy and Climate Research – Stratosphere, Research Center Jülich. We show, that the coupled approach outperforms the fully algorithmic approach by AD in terms of run time and memory requirement and argue that this can be achieved while still preserving the desireable feature of AD being automatic.

关键词： Adjoints Algorithmic Differentiation Optimization C++

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Corrigendum to 'Geometry distortions of nanostructure edges scanned with amplitude modulated atomic force microscopes'

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Measurement Science and Technology 2017年第10期28卷

作者： Dorothee Hüser Wolfgang Häßler-Grohne Jonathan Hüser Physikalisch-Technische Bundesanstalt Bundesallee 100 D-38116 Braunschweig Germany Software and Tools for Computational Engineering RWTH Aachen University Seffenter Weg 23 D-52074 Aachen Germany

In Hüser et al (2013 Meas. Sci. Technol. 24 115008), we have realized two errors in the calculations of the effect of damping in the vicinity of the surface. The error did not have a quantitatively visible impact...

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Higher-order discrete adjoint ODE Solver in C++ for dynamic optimization

Higher-order discrete adjoint ODE Solver in C++ for dynamic ...

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15th Annual International Conference on computational Science, ICCS 2015

作者： Lotz, Johannes Naumann, Uwe Hannemann-Tamás, Ralf Ploch, Tobias Mitsos, Alexander RWTH Aachen Software and Tools for Computational Engineering Aachen Germany RWTH Aachen Process Systems Engineering Aachen Germany

Parametric ordinary differential equations (ODE) arise in many engineering applications. We consider ODE solutions to be embedded in an overall objective function which is to be minimized, e.g. for parameter estimation. For derivative-based optimization algorithms adjoint methods should be used. In this article, we present a discrete adjoint ODE integration framework written in C++ (NIXE 2.0) combined with Algorithmic Differentiation by overloading (dco/c++). All required derivatives, i.e. Jacobians for the integration as well as gradients and Hessians for the optimization, are generated automatically. With this framework, derivatives of arbitrary order can be implemented with minimal programming effort. The practicability of this approach is demonstrated in a dynamic parameter estimation case study for a batch fermentation process using sequential method of dynamic optimization. Ipopt is used as the optimizer which requires second derivatives. © The Authors. Published by Elsevier B.V.

关键词： Ordinary differential equations

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MPI-Parallel Discrete Adjoint OpenFOAM

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Procedia Computer Science 2015年 51卷 19-28页

作者： Markus Towara Michel Schanen Uwe Naumann Software and Tools for Computational Engineering RWTH Aachen University Aachen Germany

OpenFOAM is a powerful Open-Source (GPLv3) computational Fluid Dynamics tool box with a rising adoption in both academia and industry due to its continuously growing set of features and the lack of license costs. Our previously developed discrete adjoint version of OpenFOAM allows us to calculate derivatives of arbitrary objectives with respect to a potentially very large number of input parameters at a relative (to a single primal flow simulation) computational cost which is independent of that number. Discrete adjoint OpenFOAM enables us to run gradient-based methods such as topology optimization efficiently. Up until recently only a serial version was available limiting both the computing performance and the amount of memory available for the solution of the problem. In this paper we describe a first parallel version of discrete adjoint OpenFOAM based on our adjoint MPI library.

关键词： OpenFOAM Adjoints MPI Algorithmic Differentiation

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Second-order Tangent Solvers for Systems of Parameterized Nonlinear Equations

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Procedia Computer Science 2015年 51卷 231-238页

作者： Niloofar Safiran Johannes Lotz Uwe Naumann LuFG Informatik 12: Software and Tools for Computational Engineering RWTH Aachen University Germany

Forward mode algorithmic differentiation transforms implementations of multivariate vector functions as computer programs into first directional derivative (also: first-order tangent) code. Its reapplication yields higher directional derivative (higher-order tangent) code. Second derivatives play an important role in nonlinear programming. For example, second-order (Newton-type) nonlinear optimization methods promise faster convergence in the neighborhood of the minimum through taking into account second derivative information. Part of the objective function may be given implicitly as the solution of a system of n parameterized nonlinear equations. If the system parameters depend on the free variables of the objective, then second derivatives of the nonlinear system's solution with respect to those parameters are required. The local computational overhead for the computation of second-order tangents of the solution vector with respect to the parameters by Algorithmic Differentiation depends on the number of iterations performed by the nonlinear solver. This dependence can be eliminated by taking a second-order symbolic approach to differentiation of the nonlinear system.

关键词： Nonlinear System Second-Order Tangent Hessian Algorithmic Differentiation Symbolic Differentiation

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Higher-order Discrete Adjoint ODE Solver in C++ for Dynamic Optimization

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Procedia Computer Science 2015年 51卷 256-265页

作者： Johannes Lotz Uwe Naumann Ralf Hannemann-Taḿas Tobias Ploch Alexander Mitsos RWTH Aachen Software and Tools for Computational Engineering Aachen Germany RWTH Aachen Process Systems Engineering Aachen Germany

Parametric ordinary differential equations (ODE) arise in many engineering applications. We consider ODE solutions to be embedded in an overall objective function which is to be minimized, e.g. for parameter estimation. For derivative-based optimization algorithms adjoint methods should be used. In this article, we present a discrete adjoint ODE integration framework written in C + + (NIXE 2.0) combined with Algorithmic Differentiation by overloading (dco/c + +). All required derivatives, i.e. Jacobians for the integration as well as gradients and Hessians for the optimization, are generated automatically. With this framework, derivatives of arbitrary order can be implemented with minimal programming effort. The practicability of this approach is demonstrated in a dynamic parameter estimation case study for a batch fermentation process using sequential method of dynamic optimization. Ipopt is used as the optimizer which requires second derivatives.

关键词： Adjoints ODE Algorithmic Differentiation Dynamic Optimization C + +

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Development of a discrete adjoint CFD code using algorithmic differentiation by operator overloading 1

Development of a discrete adjoint CFD code using algorithmic...

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1st International Conference on engineering and Applied Sciences Optimization, OPT-i 2014

作者： Dastouri, Z. Lotz, J. Naumann, U. RWTH Aachen University Software and Tools for Computational Engineering AachenD-52062 Germany

ISBN: (纸本)9789609999465

Design optimization for fluid flow recently has drawn a great deal of attention in the industrial design area including aeronautic[1, 2], turbo-machinery[3] and automotive design[4, 5]. The optimization problem is subject to a large number of design variables that makes calculating the sensitivity derivatives by finite differences a costly procedure. Algorith- mic differentiation(AD) is a well known method to differentiate the computer program with the aim of obtaining the sensitivity of the objective with respect to design variables. There are two different AD approaches, operator overloading and source transformation. In this paper we describe a design framework for application of the algorithmic differentiation tool by operator overloading in Fortran dco/fortran1 to CFD analysis solver called GPDE2. GPDE is an un- structured pressure-based steady Navier-Stokes code with finite volume spatial discretization, which is based on the SIMPLE pressure-correction scheme for the incompressible viscous flow computation. This approach yields a discrete tangent-linear and adjoint version of the CFD code. Moreover, we address typical implementation issues and complexities in the differentia- tion procedure by AD tool in the CFD code. The numerical results of a relevant test case by our overloading tool in forward and reverse mode are compared with their corresponding results of the previously differentiated code by source transformation that is generated by TAPENADE. We show that in terms of ease of implementation and ability to handle arbitrary functions, dco/- fortran provides the differentiated code with a greater flexibility and robustness in comparison with AD by source transformation. This research is aimed toward the application of AD tools by operator overloading on a legacy industrial incompressible flow solver that is in our context ESI? ACE+.

关键词： Sensitivity analysis

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Towards tangent-linear GPU programs using OpenACC

Towards tangent-linear GPU programs using OpenACC

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4th Symposium on Information and Communication Technology, SoICT 2013

作者： Minh, Bui Tat Förster, Michael Naumann, Uwe Bangkok Thailand LuFG Informatik 12: Software and Tools for Computational Engineering RWTH Aachen University Aachen Germany

ISBN: (纸本)9781450324540

Recently, Graphics Processing Units(GPUs) have emerged as a very promisingly powerful resource in scientific computing. Algorithmic Differentiation is a technique to numerically evaluate first and higher derivatives of a function specified by a computer program efficiently up to machine precision. Derivative programs which are used to compute derivatives of functions are so-called tangent-linear program and adjoint program. This paper aims to offload any particular independent loop in tangent-linear program to GPUs. The proposed technique is OpenACC APIs for annotating an independent loop to be executed in parallel on GPUs. Our case study for OpenACC tangent-linear code shows an enormous speedup. OpenACC shows its simplicity of accelerating tangent-linear code by hiding the data movement between CPU and GPU memory. Copyright © 2013 ACM.

关键词： Program processors

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Discrete adjoints of PETSc through dco/c++ and adjoint MPI

Discrete adjoints of PETSc through dco/c++ and adjoint MPI

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19th International Conference on Parallel Processing, Euro-Par 2013

作者： Lotz, Johannes Naumann, Uwe Sagebaum, Max Schanen, Michel LuFG Informatik 12: Software and Tools for Computational Engineering RWTH Aachen University Germany Department of Mathematics Center for Computational Engineering Science RWTH Aachen University Germany

ISBN: (纸本)9783642400469

PETSc's [1] robustness, scalability and portability makes it the foundation of various parallel implementations of numerical simulation codes. We formulate a least squares problem using a PETSc implementation as the model function and rely on adjoint mode Algorithmic Differentiation (AD) [2] for the accumulation of the derivative information. Various AD tools exist that apply the adjoint model to a given C/C++ code, while none is able to differentiate MPI [3] enabled code. We solved this by combining dco/c++ and the Adjoint MPI library, leading to a fully discrete adjoint implementation of PETSc. We want to underline that this work differs from accumulating derivative information through AD for PETSc algorithms (see e.g. [4]). We compute derivative information of PETSc itself opening up the possibility of an enclosing optimization problem (as needed, e.g., by [5]). © 2013 Springer-Verlag.

关键词： Codes (symbols)

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A Discrete Adjoint Model for OpenFOAM

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Procedia Computer Science 2013年 18卷 429-438页

作者： M. Towara U. Naumann Software and Tools for Computational Engineering RWTH Aachen University 52056 Aachen Germany

We present a discrete adjoint version of the open-source fluid-dynamics package OpenFOAM obtained by operator overloading which yields, in comparison to continuous adjoint versions, a greater flexibility and robustness. We discuss our implementation and how the discrete adjoint version of OpenFOAM differs from existing continuous implementations. To reduce the inherent memory requirement of discrete adjoint code we introduce a checkpointing scheme to trade computation time for memory. Moreover we show results from a relevant reference case.

关键词： CFD OpenFOAM Discrete adjoints Shape optimization

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