Location
MC 5479
Candidate
Anand Karki| Applied Mathematics, University of Waterloo
Title
Data-Driven Mobile Sensor Planning and Interpretation
Abstract
Accurate reconstruction of an unsteady flow from a small number of measurements depends critically on where those measurements are collected. Fixed Eulerian sensors may miss structures that move through the domain, while passively advected Lagrangian sensors may become concentrated in only a subset of the dynamics. This thesis develops two complementary data-driven approaches for designing and interpreting mobile sensing strategies using only offline snapshot data.
The first contribution extends Proper Orthogonal Decomposition with column-pivoted QR factorization (POD--QR) from static sensor placement to mobile sensor trajectory planning. A sequence of sliding temporal windows is used to identify time-varying POD--QR target locations. These unordered targets are connected into consistent multi-sensor trajectories using minimum-distance assignment, and the resulting sensor motion is constrained by a prescribed maximum speed. Across the Lamb--Oseen vortex, double-gyre advection, forced Kolmogorov turbulence, and cylinder vortex shedding, the resulting Moving POD--QR strategy improves reconstruction accuracy relative to fixed Eulerian and passively advected Lagrangian sensing at practical sensor counts.
Although these trajectories determine where a small number of sensors should move, they provide only a sparse view of the sensing objective and are therefore difficult to interpret over the full domain. The second contribution introduces the Information Flow Field, or InfoFlo, a dense time-varying vector field that represents locally preferred sensing motion. InfoFlo is constructed by applying POD--QR independently over overlapping space--time regions and converting each locally selected measurement location into a displacement direction. Comparisons using cosine similarity, divergence, and finite-time Lyapunov exponents show that the resulting sensing-induced geometry often differs from material transport. Together, Moving POD--QR and InfoFlo provide a model-free framework for both generating informative mobile sensor trajectories and understanding the spatial structures that drive them.