Non-parametric modelling and simulation of spatiotemporally varying geo-data

Modelling and simulation of spatially or temporally varying geo-data play a pivotal role in the development of digital twins of civil infrastructures and smart cities. Measurements on geo-data are however often sparse, and it is challenging to model or simulate the spatiotemporally varying geo-data directly from sparse measurements. Non-parametric methods are appealing to tackle this challenge because they bypass the difficulty in the selection of suitable parametric models or function forms and offer great flexibility for mimicking complicated characteristics of geo-data in a data-driven manner. This paper provides a state-of-the-art review of non-parametric modelling and simulation of spatiotemporally varying geo-data under the framework of spectral representation or compressive sensing/sampling (CS). Similarity and differences between the spectral representation-based methods and the CS-based methods are discussed, including modelling of unknown trend function, marginal probability density function (PDF), and spatial or temporal autocovariance structure. Advantages of the CS-based methods are highlighted, such as superior performance for sparse measurements (i.e. capable of dealing with a sampling frequency lower than Nyquist frequency) and incorporation of the uncertainty associated with the interpretation of sparse measurements. Numerical examples are presented to demonstrate both spectral representation-based methods and CS-based methods.