Development of Neural Networks for Mineral Layer Surface Reconstruction and Assessment of Key Geological Characteristics Spatial Distribution

Abstract This article examines the sequential reconstruction of a mineral productive-layer surface and the qualitative geological parameter distributed across it from incomplete and noisy spatial data. A software package has been developed to generate synthetic surfaces and parameter fields, introduce controlled distortions, form training samples and compare neural network results with those obtained using classical interpolation methods. In the first stage a fully connected neural network approximates the signed vertical distance. The surface is determined by the zero level of the resulting implicit function constructed according to the Signed Distance Function (SDF) principle. The maximum number of training epochs was 200. In the second stage a coordinate-based multilayer perceptron (MLP) uses sparse measurements to reconstruct a continuous qualitative-parameter field on the reconstructed surface. The effects of number of observations, coordinate noise, parameter noise, local data gaps and hidden regions were investigated. Classical methods yielded lower Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) values on a smooth surface. For a vertical discontinuity, the SDF model had the lowest MAE across the entire range studied and achieved a lower RMSE when the number of points was small. In the case of local gaps SDF model showed the lowest RMSE and MAE. In the experiment with a large hidden region, linear interpolation yielded the best overall RMSE. The second neural network maintained a constant error as parameter noise increased and enabled rapid re-computation of the field after training. However, smoothed radial basis function (RBF) interpolation yielded a lower RMSE than the neural network. The results of the study show that the neural network approach does not have a universal advantage over common interpolation methods and should be based on the data structure, required accuracy, and expected recalculation frequency.