Abstract

Understanding the governing equations of biological filament dynamics is essential for predicting cellular behavior, yet these equations are often difficult or impossible to derive directly from first principles. This thesis investigates the use of Sparse Identification of Nonlinear Dynamics (SINDy) as a unified, data-driven framework for discovering, validating, and refining governing equations from both simulated and experimental data. Focusing on biological filament processes, including growth, disassembly, and severing, this work is designed not only to apply SINDy, but to systematically demonstrate that it is a reliable and generalizable tool for modeling complex biophysical systems. To establish this, SINDy is first applied to systems with known governing equations, serving as a validation step to show that the method can accurately recover true underlying dynamics. Using simulated datasets from established filament models, SINDy consistently identifies the correct functional forms and parameters, confirming that it works as intended in controlled settings. Building on this foundation, the method is then applied in a hybrid model-development framework, where partial theoretical equations exist but are incomplete or imperfect. In these cases, SINDy is used to assess, refine, and improve existing models by identifying missing or misrepresented terms, demonstrating its ability to enhance traditional modeling approaches. Finally, SINDy is applied to experimental filament data where no governing equations are known. Through the construction of candidate function libraries and the use of sparse regression, the method generates interpretable equations directly from observed data, revealing underlying dynamics and suggesting new biological insights. Overall, this work demonstrates that SINDy is not only effective in controlled scenarios but is a robust, flexible, and broadly applicable tool that can be used to analyze, validate, and discover models in biological filament systems and beyond, highlighting its potential for widespread use in complex scientific settings.

Publication Date

5-7-2026

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

Mathematics and Statistics, School of

College

College of Science

Advisor

Lishibanya Mohapatra

Advisor/Committee Member

Nishant Malik

Advisor/Committee Member

Laura Munoz

Campus

RIT – Main Campus

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