Date of Award
Doctor of Philosophy in Mathematical Sciences - (Ph.D.)
Anand Uttam Oza
Data-driven modeling seeks to extract a parsimonious model for a physical system directly from measurement data. One of the most interpretable of these methods is Sparse Identification of Nonlinear Dynamics (SINDy), which selects a relatively sparse linear combination of model terms from a large set of (possibly nonlinear) candidates via optimization. This technique has shown promise for synthetic data generated by numerical simulations but the application of the techniques to real data is less developed. This dissertation applies SINDy to video data from a bio-inspired system of mictrotubule-motor protein assemblies, an example of nonequilibrium dynamics that has posed a significant modelling challenge for more than a decade. In particular, we constrain SINDy to discover a partial differential equation (PDE) model that approximates the time evolution of microtubule orientation. The discovered model is relatively simple but reproduces many of the characteristics of the experimental data. The properties of the discovered PDE model are explored through stability analysis and numerical simulation; it is then compared to previously proposed models in the literature.
Chapter 1 provides an introduction and motivation for pursuing a data driven modeling approach for active nematic systems by introducing the Sparse Identification of Nonlinear Dynamics (SINDy) modeling procedure and active nematic systems. Chapter 2 lays the foundation for modeling of active nematics to better understand the model space that is searched. Chapter 3 gives some preliminary considerations for using the SINDy algorithm and proposes several approaches to mitigate common errors. Chapter 4 treats the example problem of rediscovering a governing partial differential equation for active nematics from simulated data including some of the specific challenges that arise for discovery even in the absence of noise. Chapter 5 details the procedure for extracting data from experimental observations for use with the SINDy procedure and details tests to validate the accuracy of the extracted data. Chapter 6 presents the active nematic model extracted from experimental data via SINDy, compares its properties with previously proposed models, and provides numerical results of its simulation. Finally, Chapter 7 presents conclusions from the work and provides future directions for both active nematic systems and data-driven modeling in related systems.
Robertson, Connor, "Continuum modeling of active nematics via data-driven equation discovery" (2023). Dissertations. 1670.