Automatic differentiation algorithms in model analysis

Title: Automatic differentiation algorithms in model analysisAuthor: M.J. HuiskesDate: 19 March, 2002In this thesis automatic differentiation algorithms and derivative-based methods are combined to develop efficient tools for model analysis. Automatic differentiation algorithms comprise a class of algorithms aimed at the derivative computation of functions that are represented as computer code. Derivative-based methods that may be implemented using these algorithms are presented for sensitivity analysis and statistical inference, particularly in the context of nonlinear parameter estimation.Local methods of sensitivity analysis are discussed for both explicit and implicit relations between variables. Particular attention is paid to propagation of uncertainty, and to the subsequent uncertainty decomposition of output uncertainty in the various sources of input uncertainty.Statistical methods are presented for the computation of accurate inferential information for nonlinear parameter estimation problems by means of higher-order derivatives of the model functions. Methods are also discussed for the assessment of the appropriateness of model structure complexity in relation to quality of data.To realize and demonstrate the potential of routines for model analysis based on automatic differentiation a software library is developed: a C++ library for the analysis of nonlinear models that can be represented by differentiable functions in which the methods for parameter estimation, statistical inference, model selection and sensitivity analysis are implemented. Several experiments are performed to assess the performance of the library. The application of the derivative-based methods and the routines of the library is further demonstrated by means of a number of case studies in ecological assessment. In two studies, large parameter estimation procedures for fish stock assessment are analyzed: for the Pacific halibut and North Sea herring species. The derivative-based methods of sensitivity analysis are applied in a study on the contribution of Russian forests to the global carbon cycle.