Sampling Gaussian stationary random fields: A stochastic realization approach.

Area of Science:

• Geosciences
• Computational Mathematics
• Engineering

Background:

• Generating large-scale samples of stationary random fields is vital for geomaterial modeling and uncertainty quantification.
• Traditional covariance matrix decomposition methods are computationally expensive, especially for high-dimensional random fields.

Purpose of the Study:

• To propose an efficient stochastic realization approach for sampling Gaussian stationary random fields.
• To develop a computationally cheaper alternative to traditional methods for generating random field samples.

Main Methods:

• Developed an efficient stochastic realization approach using systems and control theory.
• Constructed rational spectral densities and obtained autoregressive moving-average (ARMA) models via spectral factorization for exponential and squared exponential covariance functions.
• Integrated the method for multiscale simulations, enabling sample interpolation at finer scales.

Main Results:

• Generated samples of Gaussian stationary random fields efficiently in the space domain using low-order ARMA models.
• Demonstrated computational efficiency compared to covariance matrix decomposition methods.
• Successfully applied the method to multiscale simulations with accurate sample interpolation.

Conclusions:

• The proposed ARMA-based stochastic realization approach offers a computationally efficient and favorable alternative for sampling Gaussian stationary random fields.
• This method significantly reduces computational cost, making it suitable for large-scale and multiscale applications in fields like geomaterial modeling.