Inferring potential landscapes from noisy trajectories

TL;DR

This paper introduces a Bayesian approach with structured kernel interpolation to robustly infer complex potential landscapes from noisy, sparsely sampled particle trajectories, validated on experimental data.

Contribution

It presents a novel Bayesian method that infers arbitrary-shaped potentials and measurement noise, scalable to large datasets using structured kernel interpolation.

Findings

Successfully inferred potentials from noisy trajectories

Extended analysis to large datasets with structured kernel interpolation

Validated on 1D and 2D experimental particle trajectories

Abstract

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.