Applications of automatic differentiation to compute the equilibria of dynamical systems

Marco Gambone

Scuola Superiore di Udine

Derivatives of mathematical functions play a key role in many scientific areas. To compute them we briefly present a quite recent method, namely Automatic Differentiation (AD) [1], which automatically transforms a program that calculates numerical values of a function, into a program which calculates numerical values for derivatives of that function. After that, we use ADiMat [2], a MATLAB/Octave tool which implements AD, to compute equilibria of an epidemiological model and study their stability. We are then able to compare the difference in time complexity and accuracy between AD and other classical techniques calculating derivatives. This seminar concerns the results of Marco’s BSc thesis. [1]A. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, 2008, doi: 10.1137/1.9780898717761. [2]C. H. Bischof, H. M. Bücker, B. Lang, A. Rasch, and A. Vehreschild, Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs, in Proceedings of the Second IEEE International Workshop on Source Code Analysis and Manipulation (SCAM 2002), IEEE Computer Society, Los Alamitos, CA, 2002, doi: 10.1109/SCAM.2002.1134106, pp. 65–72.