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Many studies apply sensitivity analysis to explore the impact of reaction kinetic parameters on model predictions. The importance of thermochemical and transport data is often assumed to be relatively low. While this is true for specific combustion properties of hydrocarbons, the role of thermochemical and transport data in combustion processes of nitrogen-containing molecules remains to be investigated. Thus, this work applies adjoint sensitivity analysis to the complete set of parameters in combustion models, i.e., kinetics, thermodynamics, and transport data. This integral approach increases the number of parameters considered in the sensitivity analysis drastically. Compared to forward sensitivity analysis, the adjoint approach is very efficient for a large number of parameters, and analysis with several thousand parameters can be performed in seconds. Nitrogen oxide formation in methane/air flames and laminar burning velocities of ammonia/air flames are considered as prediction targets. Sensitivity analysis results for kinetic, thermochemical, and transport data are compared by jointly considering all appearing parameter uncertainties. The comparison reveals that, due to their importance for the equilibrium constants of elementary reactions, the optimization potential of thermodynamic properties is often similarly high as that of the kinetics parameters. Transport parameters are found to be of the lowest priority for the model development due to their low uncertainties, even though high sensitivities are determined for several of them. More specifically, the analysis for the laminar burning velocities of ammonia/air flames reveals a high optimization potential for parameters in the N 2 -amine chemistry, including the molar heat capacities of N 2 H 2 , N 2 H 3 , and NH. Interestingly, analyses with different mechanisms reveal strongly diverging results, especially regarding the importance of reactions with OH, which is uncommon when considering the combustion of hydrocarbons. [ABSTRACT FROM AUTHOR]

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 are coupled with 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. [ABSTRACT FROM AUTHOR]

Adjoint mode algorithmic (also know as automatic) differentiation (AD) transforms implementions of multivariate vector functions as computer programs into first-order adjoint code. Its reapplication or combinations with tangent mode AD yields higher-order adjoint 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. The adjoint mode is of particular interest in large-scale gradient-based nonlinear optimization due to the independence of its computational cost on the number of free variables. 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 as well as the additional memory requirement for the computation of second-order adjoints of the solution vector with respect to the parameters by AD depends on the number of iterations performed by the nonlinear solver. This dependence can be eliminated by taking a symbolic approach to the differentiation of the nonlinear system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: Algorithmic differentiation (AD) is a mathematical concept which evolved over the last decades to a very robust and well understood tool for computation of derivatives. It can be applied to mathematical algorithms, codes for numerical simulation, and whenever derivatives are needed. In this paper we report on the algorithmic differentiation of the discontinuous Galerkin solver padge, a large and complex code written in C++ with underlying external libraries. The reports on successful application of AD to large scale codes are rare in literature and up to now this is not state of the art. Most of the codes, which are differentiated nowadays, are written in C or Fortran. The padge code was differentiated with the operator overloading tool dco/c++ in forward as well as reverse mode. The differentiated code is validated and runs in the expected time margins of AD. [Copyright &y& Elsevier]

Abstract: An essential performance and correctness factor in numerical simulation and optimization is access to exact derivative information. Adjoint derivative models are particularly useful if a function’s number of inputs far exceeds the number of outputs. The propagation of adjoints requires the data flow to be reversed, implying the reversal of all communication in programs that use message-passing. This paper presents recent advances made in developing the adjoint MPI library AMPI. The described proof of concept aims to serve as the basis for coupling other overloading AD tools with AMPI. We illustrate its use in the context of a specific overloading tool for algorithmic differentiation (AD) for C++ programs. A simplified but representative application problem is discussed as a case study. [ABSTRACT FROM AUTHOR]

Abstract: We describe the use of first- and second-order tangent-linear and adjoint models of the residual of linear-implicit autonomous differential algebraic systems in the context of an extrapolated Euler scheme. The derivative code compiler dcc is applied to a C-implementation of the residual to get first derivative code. Second-(and higher-)order derivative models are obtained by reapplication of dcc to its own output. The resulting solver serves as a first proof of concept of a new platform for source-level manipulation of mathematical models that is currently under development at RWTH Aachen University. [ABSTRACT FROM AUTHOR]

Abstract: Goal oriented dual weight error estimation has been used in context of computational fluid dynamics for several years. The adaptation of this method to geophysical models is the subject of this paper. A differentiation-enabled prototype of the NAG Fortran compiler is used to generate a discrete adjoint version of such a geophysical model and allows to compute the required goal sensitivities. Numerical results are presented for a shallow water configuration of the Icosahedral Non-hydrostatic General Circulation Model (ICON). A special treatment of the underlying linear solver is discussed yielding improved scalability of this approach and a significant reduction in memory consumption and runtime. [ABSTRACT FROM AUTHOR]

Abstract: Runs of numerical computer programs can be visualized as directed acyclic graphs (DAGs). We consider the problem of restoring the intermediate values computed by such a program (the vertices in the DAG) in reverse order for a given upper bound on the available memory. The minimization of the associated computational cost in terms of the number of performed arithmetic operations is shown to be NP-complete. The reversal of the data-flow finds application, for example, in the efficient evaluation of adjoint numerical programs. We derive special cases of numerical programs that require the intermediate values exactly in reverse order, thus establishing the NP-completeness of the optimal adjoint computation problem. Last but not least we review some state-of-the-art approaches to efficient data-flow reversal taken by existing software tools for automatic differentiation. [Copyright &y& Elsevier]