Owen Hughes

Mikhail Genkin, Owen Hughes, Tatiana A. Engel

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system's dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain.

Henry O. Jacobs, Owen K. Hughes, Matthew Johnson-Roberson et al.

The success of autonomous systems will depend upon their ability to safely navigate human-centric environments. This motivates the need for a real-time, probabilistic forecasting algorithm for pedestrians, cyclists, and other agents since these predictions will form a necessary step in assessing the risk of any action. This paper presents a novel approach to probabilistic forecasting for pedestrians based on weighted sums of ordinary differential equations that are learned from historical trajectory information within a fixed scene. The resulting algorithm is embarrassingly parallel and is able to work at real-time speeds using a naive Python implementation. The quality of predicted locations of agents generated by the proposed algorithm is validated on a variety of examples and considerably higher than existing state of the art approaches over long time horizons.