Biological Models’ Parameter Estimation Based on Discrete Measurements and Adjoint Sensitivity Analysis
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Mathematical models of biological processes are usually continuous time (CT) and take the form of non-linear ordinary differential equations. On the other hand the estimation of model parameters is done based on discrete time (DT), relatively rare, measurements. Hence, overall problem of parameter estimation has hybrid, continuous-discrete form: it uses CT model and minimise DT performance index depending on DT prediction errors. In our previous works we have published Generalized Back Propagation Through Time (GBPPT) method—a method allowing us to use the adjoint sensitivity analysis for obtained hybrid system, and giving as a result a computationally effective recipe for calculating gradient of the performance index in parameter space. GBPTT specifies rules for construction of the adjoint system, in particular it specifies how to manage elements interfacing between CT and DT parts of the system: ideal sampler (IS) and ideal pulser (IP). Such rules for isolated IS and IP elements has been proposed without strict formal rationale. In this article we deliver a proof of correctness of such rules. Additionally, as an illustration, we present an example of application of GBPTT to parameter estimation of chemical enzymatic reaction which is one of basic biochemical reaction.
KeywordsParameter estimation Sensitivity analysis Ordinary differential equations
This work was supported by the Silesian University of Technology and by the Polish National Science Centre under grants UMO-2018/29/B/ST7/02550 (K.F.), DEC-2016/21/B/ST7/02241 (K.Ł.). Calculations were performed using the infrastructure supported by the computer cluster Ziemowit (https://www.ziemowit.hpc.polsl.pl/en/) funded by the Silesian BIO-FARMA project No. POIG.02.01.00-00-166/08 and expanded in the POIG.02.03.01-00-040/13 in the Computational Biology and Bioinformatics Laboratory of the Biotechnology Centre at the Silesian University of Technology.
- 1.Fujarewicz, K., Gałuszka, A.: Generalized backpropagation through time for continuous time neural networks and discrete time measurements. Lecture Notes in Computer Science, pp. 190–196. Springer, Heidelberg (2004)Google Scholar
- 2.Fujarewicz, K.: Optimal discrete-time control of continuous-time systems with fractional order hold. In: Proceedings of 4th International Carpathian Control Conference, Slovakia , pp. 857-860 (2003)Google Scholar
- 3.Fujarewicz, K.: Adjoint sensitivity analysis for identification of continuous-time models based on discrete-time measurements. In: Proceedings of 11th International Conference on Methods and Models in Automation and Robotics, Miȩdzyzdroje, Poland, pp. 519–524 (2005)Google Scholar
- 6.Łakomiec, K., Fujarewicz, K.: Parameter estimation of non-linear models using adjoint sensitivity analysis. In: Sobecki, J., Boonjing, V., Chittayasothorn, S. (eds.) Advanced Approaches to Intelligent Information and Database System, pp. 59–68. Springer, Heidelberg (2014)Google Scholar