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.

中文翻译：

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局部和因果相互作用的场动力学推断

从观测数据推断时空定义的领域是许多科学领域的核心学科。这项工作在贝叶斯框架中解决了这个问题。所提出的方法基于在空间和时间上定义的统计均匀随机字段，并演示了如何从数据中重建字段及其先验相关结构。相关结构的先验模型以非参数的方式描述，仅建立在基本物理假设（例如时空同质性，局部性和因果关系）的基础上。这些假设足以从单个过程实现的嘈杂数据和不完整数据成功地推断出该领域及其先前的相关结构，如通过多个数值示例所示。