Nonlinear identification of cancer tumour dynamic model using data-driven methods with control

Abstract

Data-driven modeling has rapidly emerged as a prominent tool in modelling complex biological systems. This paper delves into the application of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Dynamic Mode Decomposition with control (DMDc) to identify the underlying nonlinear dynamics of a cancer tumour model. The primary objective was to assess the algorithm's efficacy in identifying the complicated dynamics of such systems. Results showed that the SINDy algorithm remarkably captures state variables of the system, especially those that display polynomial or linear behaviour. It demonstrates significant alignment with the actual mathematical model, highlighting its potential in modelling complex systems. The findings confirm the potential of SINDy as a formidable tool in biological data-driven modelling. The study also suggests that further refinements in the library matrix and the inclusion of domain-specific knowledge could potentially enhance the accuracy of the algorithm, making it an invaluable asset in nonlinear identification of dynamical systems.