Kyle Nguyen, North Carolina State University
Integrating Mathematical Modeling with Machine Learning Approaches with Applications in Brain Cancer and Infectious Disease
In our recent studies, we highlight the importance of integrating mathematical modeling with machine learning techniques to help understanding the underlying biological systems. Part One: We propose a novel model represented by a system of two partial differential equations (PDEs) that incorporates both cell proliferation and migration. This model demonstrates a superior fit to experimental data compared to simpler PDE models, revealing strong correlations between traveling-wave speeds and population heterogeneity. Additionally, we identify a subset of cell lines that align with a “Go-or-Grow”-type model and explore correlations between fitted model parameters and patient age and survival outcomes. Part Two: Agent-based models (ABMs) have emerged as effective tools for studying infectious diseases by incorporating heterogeneity and stochasticity through individual agent behaviors. However, calibrating ABMs and performing uncertainty quantification can be challenging. Ordinary differential equations (ODEs) are often used to model average population behaviors, providing a deterministic approach that simplifies calibration. To bridge the gap between ODE and ABM models, we use universal differential equations (UDEs) as approximation models that preserve the foundational ODE capturing disease dynamics while integrating neural networks to approximate local behaviors inherent to ABMs.
Please join via Zoom: https://iastate.zoom.us/j/96940388489?pwd=cztb7TbtXfSbIFS2X9oJWV3xsfT70H.1