A major challenge in the study of biological systems is that of model discovery: turning data into reduced order models that are not just predictive, but provide insight into the nature of the underlying system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data. Such data-driven methods can be used in the biological sciences where rich data streams are affording new possibilities for the understanding and characterization of complex, networked systems. In neuroscience, for instance, the integration of these various concepts (reduced-order modeling, equation-free, machine learning, sparsity, networks, multi-scale physics and adaptive control) are critical to formulating successful modeling strategies that perhaps can say something meaningful about experiments. These methods will be demonstrated on a number of neural systems. I will also highlight how such methods can be used to quantify cognitive and decision-making deficits arising from neurodegenerative diseases and/or traumatic brain injuries (concussions).
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- Mathematical Biology and Ecology Seminar