SFU Applied & Computational Math Seminar Series: Daniel Messenger

Data-driven modeling refers to the use of measurement data to infer the parameters and structure of a mathematical model. Motivated by problems in collective cell biology, this talk will explore algorithms which automate the map from experimental data to governing differential equations, specifically using weak formulations of the dynamics. We will show that the weak form is an ideal framework for identifying models from data if the performance criteria are robustness to data corruptions, highly accurate model recovery when corruption levels are low, and computational efficiency. We will demonstrate the superiority of the resulting weak-form sparse identification for nonlinear dynamics algorithm (WSINDy) in the discovery of correct underlying model equations across several key modeling paradigms, including ordinary differential equations (ODEs), partial differential equations (PDEs) with state variables depending on both time and space, and interacting particle systems (IPS). We also establish feasibility of weak-form identification of PDEs from streaming data, which enables identification of time-varying coefficients and provides an alternative framework for datasets in higher dimensions (specifically 3 space + 1 time). We will conclude with an overview of possible next directions, paying specific attention to the potential for inference of models for collective cellular migration.