Field Dynamics Inference for Local and Causal Interactions

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