A neural-process framework for stochastic simulation of spatially dependent geoscientific fields

Abstract. Geostatistical simulation (e.g., sequential Gaussian simulation, SGSim) provides an effective framework for quantifying variability of geoscientific variables and supporting risk-informed decision-making in various scenarios. These approaches are theoretically well grounded under assumptions such as stationarity and Gaussianity, and their practical implementation typically involves explicit variogram modeling and repeated neighborhood-based computations, which may become demanding in large-scale or high-dimensional settings. Recently, data-driven modeling strategies have gained increasing attention across scientific disciplines, offering flexible mechanisms for learning spatial dependence structures directly from data. This development motivates the exploration of learning-based alternatives for stochastic simulation. In this paper, artificial neural network-based models were constructed to address the above issues. A series of simulation experiments was generated to test and validate the proposed model. Our results suggest that: (1) spatial dependence can be captured by two complementary strategies, using neighboring attributes (e.g., spatial lag features) and encoding relative positions (e.g., MEM); (2) within our experiments, the proposed data-driven model appears less sensitive to non-Gaussianity and non-stationarity; and (3) the model provides a feasible complement to SGSim by reproducing key statistics (histogram, variogram) with favorable computational cost and flexible model configuration, particularly for large conditioning neighborhoods.