A novel methodology for geological modeling using a multilayer perceptron with supervised learning based on an implicit approach

This article presents a novel methodology for geological unit modeling, inspired by the theoretical conception of implicit geological modeling, but extending its capacity to incorporate covariates through a supervised learning method such as multi-layer perceptron. Based on a signed distance function applied to each drillhole sample, an auxiliary variable is generated which, together with spatial coordinates, is associated with the corresponding geological category. These data are used in a supervised training process, where the perceptron learns the spatial distribution of geological units. One of the main advantages of the model is the ease of incorporating covariates, allowing those with higher quality or sampling density to contribute to a more robust subsurface representation. Subsequently, both the auxiliary variable and the covariates are interpolated at the target coordinates. The trained perceptron assigns a geological class to each grid cell, and a post-processing step adjusts the contacts between units, enhancing geological continuity. The proposed methodology is validated using a synthetic dataset representing four stratified lithological units in a 2D grid. Each unit is associated with spatial coordinates and a secondary variable corresponding to rock density. From this grid, a 2.75 % sample is extracted, equivalent to 11 irregularly spaced vertical drillholes, serving as the starting point for applying the method in a controlled environment. The results are compared with those from conventional implicit modeling using precision, recall, F1-score, and Kappa coefficient metrics, showing a superior performance of the proposed method, honoring geological contacts, and improving the spatial distribution of lithological units. The findings of this study provide a foundation for scaling the methodology, exploring new machine learning models, optimizing computational performance, and extending it to real 3D scenarios.