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 statistically homogeneous random fields defined in space and time 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. This work presents a Bayesian inference method to infer space‐time homogeneous stochastic processes from noisy and incomplete observations of a single realization of the process. It relies on a reformulation in terms of external random excitations and the dynamic response of the system and performs a joint inference thereof by means of a variational approximation of the posterior.