  We propose a physics-based method to learn environmental fields (EFs) using a
mobile robot. Common purely data-driven methods require prohibitively many
measurements to accurately learn such complex EFs. Alternatively, physics-based
models provide global knowledge of EFs but require experimental validation,
depend on uncertain parameters, and are intractable for mobile robots. To
address these challenges, we propose a Bayesian framework to select the most
likely physics-based models of EFs in real-time, from a pool of numerical
solutions generated offline as a function of the uncertain parameters.
Specifically, we focus on turbulent flow fields and utilize Gaussian processes
(GPs) to construct statistical models for them, using the pool of numerical
solutions to inform their prior mean. To incorporate flow measurements into
these GPs, we control a custom-built mobile robot through a sequence of
waypoints that maximize the information content of the measurements. We
experimentally demonstrate that our proposed framework constructs a posterior
distribution of the flow field that better approximates the real flow compared
to the prior numerical solutions and purely data-driven methods.
