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Gaussian-process trend framework for efficient simulation of 3D multivariate conditional random fields
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DOI：10.1016/j.compgeo.2026.108622.png)
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Abstract
En 中文
Conditional random field simulation is widely used in site characterization, but its accuracy depends strongly on how spatial trends are represented and separated from inherent variability. Previous univariate studies showed that Gaussian process regression-based trend (t-GPR) can provide a more flexible trend representation than constant-trend and sparse Bayesian learning-based models. This study extends t-GPR to multivariate conditional random field simulation for cross-correlated geotechnical parameters. A regularized multivariate covariance representation is adopted to enable robust inference from sparse collocated observations. In the proposed framework, multivariate Gaussian process fields are used to model spatial trends, while inherent variability is modeled separately. Low-rank trend approximation and Kronecker-product algorithms are developed to enable efficient Bayesian inference and conditional simulation in three-dimensional settings. The framework is also extended to non-lattice observation data by decomposing the data into a CPT-lattice subset and remaining non-lattice observations. Three real case studies, ranging from lattice CPT-only data to sparse full 3D non-lattice CPT-borehole data, demonstrate that the proposed framework provides effective uncertainty quantification, particularly under sparse-data conditions where cross-parameter dependence can be exploited to reduce predictive uncertainty.
Keywords:
Site characterization
Variability
Trend
Multivariate random field
Gaussian process
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