Field Dynamics Inference for Local and Causal Interactions

Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on a Gaussian process prior for fields and demonstrates how to reconstruct the field together with its prior correlation structure from data. The prior model of the correlation structure is described in a non-parametric fashion and solely builds on fundamental physical assumptions such as space-time homogeneity, locality, and causality. These assumptions are sufficient to successfully infer the field and its prior correlation structure from noisy and incomplete data of a single realization of the process as demonstrated via multiple numerical examples.