David J. Gillcrist

David is a PhD candidate in Engineering and Applied Science (computational mathematics) at the University of Massachusetts Dartmouth.

His research asks how to design experiments so that the unknown parameters of a physical model can actually be recovered. Rather than treating design quality statistically, he frames it geometrically: identifiablity and numerical solvability are read from the structure of the cost manifold, using tools such as directional statistics, Weingarten spectra, and quasi-conformal scalarizations.

His current work builds reduced-basis surrogates of PDE solutions from physics-informed neural network (GPT-PINN) snapshots. The goal is to turn experimental design from a discrete choice, like selecting sensor locations from a fixed set, into a continuous optimization over the design space.

A longer-term interest is in the intersection between fractional-order dynamics and query-based problems. Particularly, when and why these dynamics arise in physical systems, and how this impacts decisions and outcomes in experiments.