| Abstract: |
| In this talk, we present a unified inverse problem framework for identifying unknown parameters and functional forms in biological PDE models using boundary, averaged, and spatial pattern data. We showcase a series of results, including boundary-driven recovery in local and nonlocal predator-prey, aggregation, and chemotaxis systems, as well as amplitude-based reconstruction from Turing patterns. Applications span across tumor-immune interactions, ecological dispersal, infectious disease modeling, cell microrheology, and microbial chemotaxis. We emphasize how diverse measurement setups -- such as boundary fluxes, time-averaged outputs, and spatial amplitudes -- enable unique and robust parameter identification across multiple biological scales. Our work bridges rigorous analytical PDE theory with realistic biological constraints, providing a principled methodology to infer mechanistic models from observed dynamics in ecology, immunology, developmental biology, and epidemiology. |
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