High-dimensional networked biological systems are ubiquitous and characterized by a large connectivity graph whose structure determines how the system operates as a whole. Our objective is to extract the underlying engineering principles of cognitive capability, namely those that allow complex networks to enact control, learning and functionality in the robust manner observed in neurosensory systems. Our models focus on the olfaction signal processing in the hawk moth and the connectomic dynamics and biomechanics of the C. elegans nematode. In addition to network structure and function, we consider a data-driven method whereby low-rank, reduced order models can be directly constructed from data alone using sparse regression algorithms. The methods can be enacted in an online and non-intrusive fashion using randomized (sparse) sampling. The method is ideal for parametric systems, requiring rapid model updates without recourse to the full high-dimensional system. Moreover, we discover Koopman embeddings, or coordinates, whereby the nonlinear dynamics can be approximated by linear evolution equations for future state prediction and control.
Nathan Kutz was awarded his B.S. in physics and mathematics from the University of Washington in 1990 and his Ph.D. in applied mathematics from Northwestern University in 1994. Following postdoctoral fellowships at the Institute for Mathematics and its Applications (University of Minnesota, 1994-1995) and Princeton University (1995-1997), he joined the University of Washington’s faculty of applied mathematics and served as chair from 2007-2015.