Non-parametric simulation of random field samples from incomplete measurements using generative adversarial networks

ABSTRACT

Random field theory is an effective tool for modelling spatial or temporal variability and uncertainty in natural phenomena, and it has been widely applied in many areas such as structural dynamics, geology, hydrology, and meteorology. Conventional methods of random field simulations are often parametric, in which explicit function forms for trend function, auto-correlation function, and marginal probability density function (PDF) should be selected, together with their corresponding parameters estimated from measurements. Complete random field measurements with many data points are indispensable for selection of the appropriate function forms and accurate estimates of their corresponding parameters. However, the measurements in practice are often incomplete. Without sufficient measurement data, the random field samples (RFSs) generated by conventional methods might contain unexpected uncertainty and might be misleading. To tackle this problem, a purely non-parametric random field simulation method is developed in this study that generates RFSs directly from incomplete measurement data using generative adversarial networks (GAN). Statistical analysis is performed to estimate statistical properties from the generated RFSs, including mean, standard deviation (SD), autocovariance function (AF), and cumulative density function (CDF). The results show that the proposed method properly simulates RFSs from incomplete measurement data in a purely data-driven manner.

KEYWORDS:

• Random field simulation
• super resolution
• Generative adversarial networks
• Incomplete measurement data

Acknowledgments

The work described in this paper was supported by grants from the Research Grant Council of Hong Kong Special Administrative Region (Project no. CityU 11202121), Shenzhen Science and Technology Innovation Commission (Shenzhen-Hong Kong-Macau Science and Technology Project (Category C) No: SGDX20210823104002020), China, Academic Research Fund (AcRF) Tier 1 Seed Funding Grant from the Ministry of Education, Singapore (Project no. RS03/23), and the Start-Up Grant from Nanyang Technological University. The financial support is gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).