Hoon Hong
Abstract
Many important real-world processes are modeled using systems of ordinary differential equations (ODEs) involving unknown parameters. The values of these parameters are usually inferred from experimental data. However, due to the structure of the model, there might be multiple parameter values that yield the same observed behavior even in the case of continuous noise-free data. It is important to detect such situations a priori, before collecting actual data. In this case, the only input is the model itself, so it is natural to tackle this question by methods of symbolic computation.
We present new software SIAN (Structural Identifiability ANalyser) that solves this problem. Our software allows to tackle problems that could not be tackled before. It is written in Maple and available at https://github.com/pogudingleb/SIAN.
- R. Bellman and K. Åström. On structural identifiability. Mathematical Biosciences, 7(3):329 -- 339, 1970. Google Scholar
Cross Ref
- G. Bellu, M. P. Saccomani, S. Audoly, and L. D'Angió. DAISY: A new software tool to test global identifiability of biological and physiological systems. Computer Methods and Programs in Biomedicine, 88(1):52-61, 2007. Google ScholarCross Ref
- H. Hong, A. Ovchinnikov, G. Pogudin, and C. Yap. Global identifiability of differential models. preprint, 2018. URL http://arxiv.org/abs/1801.08112.Google Scholar
- H. Hong, A. Ovchinnikov, G. Pogudin, and C. Yap. SIAN: software for structural identifiability analysis of ODE models. 2019. Google ScholarCross Ref
- J. Karlsson, M. Anguelova, and M. Jirstrand. An efficient method for structural identifiability analysis of large dynamic systems. IFAC Proceedings Volumes, 45(16):941 -- 946, 2012. Google ScholarCross Ref
- T. Ligon, F. Fröhlich, O. T. Chiş, J. Banga, E. Balsa-Canto, and J. Hasenauer. GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models. Bioinformatics, 34:1421--1423, 2018. Google ScholarCross Ref
- N. Meshkat, C. E.-Z. Kuo, and J. DiStefano, III. On finding and using identifiable parameter combinations in nonlinear dynamic systems biology models and COMBOS: A novel web implementation. PLOS ONE, 9:1--14, 10 2014. Google ScholarCross Ref
- R. Motwani and P. Raghavan. Randomized algorithms. Cambridge University Press, 1995.Google ScholarDigital Library
- J. Norton. An investigation of the sources of nonuniqueness in deterministic identifiability. Mathematical Biosciences, 60(1):89--108, 1982. Google ScholarCross Ref
- A. Sedoglavic. A probabilistic algorithm to test local algebraic observability in polynomial time. Journal of Symbolic Computation, 33(5):735 -- 755, 2002. Google ScholarDigital Library
- K. Thomaseth and M. P. Saccomani. Local identifiability analysis of nonlinear ODE models: How to determine all candidate solutions. IFAC-PapersOnLine, 51(2):529--534, 2018. Google ScholarCross Ref
- N. Tuncer and T. T. Le. Structural and practical identifiability analysis of outbreak models. Mathematical Biosciences, 299:1 -- 18, 2018. Google ScholarCross Ref
- A. F. Villaverde, A. Barreiro, and A. Papachristodoulou. Structural identifiability of dynamic systems biology models. PLOS Computational Biology, 12(10):1--22, 2016. Google ScholarCross Ref
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