Data-Driven Models with Expert Influence: A Hybrid Approach to Spatiotemporal Process Estimation

Abstract

In this paper, our motivating application lies in precision agriculture where accurate modeling of forage is essential for informing rotational grazing strategies. Unfortunately, a major difficulty arises in modeling forage processes as they evolve on large scales according to complex ecological influences. As robots can collect data over large scales in a forage environment, they act as a promising resource for the forage modeling problem when combined with a data-driven Gaussian processes (GPs) technique. However, GPs are nonparametric in nature and may be blind to certain nuances of a process that a parameterized expert model may predict well. Indeed, for the forage modeling problem specifically, there exist several highly parameterized models from agricultural experts that exhibit powerful predictive capabilities. Expert models, however, often come with two shortcomings: (1) parameters may be difficult to determine in general; and (2) the model may not make complete spatiotemporal predictions. For example, a stochastic differential equation (SDE) that models the dynamics of the average output of an environment may be available from experts (a typical case). In such cases, we propose to take advantage of both data-driven (GPs) and expert (SDE) models, by fusing data collected by robots, which often yields spatial insight, with models from experienced professionals that often yield temporal insights. Specifically, we propose to leverage Bayesian estimation to combine these two methods, resulting in a posterior prediction that is a hybrid of data-driven and expert models. Finally, we provide simulations to demonstrate the effectiveness of the proposed method.