Dynamic modeling and analysis of worm data via linear operator

In this thesis, we demonstrate the application of linear operator theory for data-driven dynamic modeling and analysis of worm data. In particular, Koopman and Perron-Frobenius operators are used for the dynamic modeling of two different worms namely Brugia Malayi and C elegans. Time-series data in the form of video is used to generate reduced order dynamics model to capture the moment of these two worms under different operating conditions. While the moment of the worm is in general modeled as a nonlinear dynamical system, our proposed linear operator theoretic framework provides for a linear representation of the nonlinear dynamics. The linear representation is made possible by shifting the focus from the state space to the space of functions. We exploit this linear representation for data-driven modeling of worm dynamics. For data-driven dynamic modeling, we construct a finite dimensional approximation of these linear operators. Two popular algorithms, Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) are used for the finite dimensional approximation of the linear Koopman operator from time series data. The data-driven model is used for prediction of worm dynamics and the comparison of worm movement under different operating conditions caused by the exposure of worm to different drug cocktails. The developed dynamic model will be used to understand the impact of different drug cocktails on worm moment thereby providing a systematic data-driven approach for drug discovery