  While particle trajectories encode information on their governing potentials,
potentials can be challenging to robustly extract from trajectories.
Measurement errors may corrupt a particle's position, and sparse sampling of
the potential limits data in higher-energy regions such as barriers. We develop
a Bayesian method to infer potentials of arbitrary shape alongside measurement
noise. As an alternative to Gaussian process priors over potentials, we
introduce structured kernel interpolation to the Natural Sciences which allows
us to extend our analysis to large data sets. Our method is validated on 1D and
2D experimental trajectories for particles in a feedback trap.
