# Field dynamics inference for local and causal interactions

## TL;DR

This paper presents a Bayesian method for inferring space-time fields and their correlation structures from noisy, incomplete data, based on physical assumptions like homogeneity, locality, and causality.

## Contribution

It introduces a non-parametric prior model for correlation structures that leverages fundamental physical principles to improve field inference from limited data.

## Key findings

- Successfully reconstructs fields and correlations from single noisy data realizations.
- Demonstrates robustness with incomplete and noisy observational data.
- Applicable across various scientific disciplines involving spatiotemporal data.

## Abstract

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.