What Can Ionic Transport Data Reveal About Steric Interactions?

Baoli Hao

Ph.D. candidate in Applied Mathematics, Illinois Institute of Technology

Abstract

To what extent can microscopic interactions be inferred from observable dynamics? We investigate this question in ionic transport, where steric interactions may operate at scales beyond experimental resolution. Within a unified energy-dissipation framework, we develop a hierarchy of local, higher-order, and nonlocal constitutive models to investigate what can be learned from dynamical observations. By connecting interaction scales and observational information with identifiability, model stability, and predictive accuracy, we determine the level of constitutive complexity supported by the data. Our study highlights the distinction between recovering microscopic interactions and identifying their observable dynamical effects, providing a general perspective on data-driven coarse-graining and the limits of learning multiscale physics from finite-resolution observations.

About the speaker

Baoli Hao is a Ph.D. candidate in Applied Mathematics at the Illinois Institute of Technology, advised by Professor Chun Liu. His research lies at the intersection of inverse problems and scientific machine learning, with a particular focus on learning hidden dynamical mechanisms from incomplete observational data. His work spans interacting particle systems and nonlinear partial differential equations, emphasizing structure-preserving modeling and the mathematical foundations of data-driven inference.