Learning Biological ODE Models from Time Series Data

Abstract

Biological systems modelling is a field where large amounts of time are required to model phenomena. This is because the design of mathematical models requires indepth knowledge of the underlying interactions between the modelled entities, as well as the need to conduct many iterations of modelling and cross-validation to get a good result. This thesis was written with the aim of conducting a state of the art review of recent modelling methods for biological phenomena, as well as the comparision of data preprocessing methods with respect to model extraction from time series data. We begin by briefly introducing the area of mathematical modelling, and then describe the need for more efficient and bespoke methods for the modelling of biological phenomena. We then introduce the preliminaries for the SINDy algorithm and discuss the merits of sparsity in creating parsimonious and explainable models. We then discuss the SINDy algorithm’s implementation and how it derives a model from time series measurement data. We then show an implementation of the algorithm on real-world data, and compare the effects of various filtering and smoothing techniques. Our experiment suggests that there is a degree to which the filtering of noisy real-world data improves performance, beyond which there are diminishing results.