This research examines computer and mathematical modeling of anaerobic digestion in livestock waste recycling. Various modeling approaches, including ADM1, are analyzed, and the devel-opment of a proprietary computer program based on a self-developed mathematical model is described. The proposed mathematical model of anaerobic fermentation has demonstrated effi-ciency and reliability under industrial-scale conditions. It was developed using regression analysis and correlation methods, establishing empirical relationships between biogas yield and 20, 26 key process parameters continuously measured by biosensors in real production settings. Despite a limited static dataset (only five measurement points), the model exhibited a low average ap-proximation error of 5.5% and a high determination coefficient of 0.95, confirming its accuracy and high quality. The computer program is designed for online statistical data transmission via cellular communication and the Internet, enabling the processing of large volumes of data in ac-cordance with Big Data concepts. Its architecture ensures flexibility, scalability, and precision. Furthermore, the integration of machine learning technologies is proposed to enhance the pro-gram's predictive capabilities, leveraging Big Data analytics. The proposed computer–mathematical model is thus considered a practical, accurate, and scalable solution for monitor-ing and optimizing industrial-scale anaerobic digestion processes, combining empirical modeling with modern data processing technologies.

This study proposes a hybrid computational model for diagnosing such biases using groundwater observation data across Kazakhstan. The analytical dataset included 2402 georeferenced observations, including 492 natural springs from OpenStreetMap (OSM), 109 boreholes from OSM, and 1801 spatially filtered pseudo-absence observations. Springs and boreholes together formed 601 positive groundwater observations, while pseudo-absence samples represented a spatially filtered background level rather than confirmed groundwater absence. Each observation was characterized by 89 environmental predictors extracted from Google Earth Engine. The proposed hybrid observation source bias index (HOSBI) combines a normalized robust effect size based on the median absolute value of the Cliff delta, multivariate distribution divergence quantified using RBF-MMD, and spatially confirmed source distinctiveness. These components were assigned fixed weights of 0.40, 0.35, and 0.25 to emphasize statistical and distributional data while maintaining spatial validation. Spatial cross-validation achieved a balanced accuracy of 0.855 for distinguishing OSM sources from OSM wells and 0.846 for separating positive observations from background pseudo-absences. Climate showed the strongest source-related bias (HOSBI = 0.923), while Sentinel-1 SAR contributed the most to the contrast between positive and background data (HOSBI = 0.923). The proposed framework provides an interpretable and replicable preliminary assessment of source bias in heterogeneous geospatial datasets.

This study proposes a method for probabilistic time-series forecasting on graphs incorporating interpolation (IA-GTPF)—a decision-tree-based ensemble approach that combines observation quality metrics, historical load dynamics, information on neighboring nodes, residual correction, quantile regression, and conformal calibration. The method’s performance was evaluated using the Open Power System Data Household dataset. Fixed time boundaries defined distinct periods for training, validation, calibration, and testing. Only information available at the time of forecasting was used as input, while graph weights and preprocessing parameters were determined solely based on the training set. A separate calibration period was used to adjust confidence interval boundaries without altering point forecasts. On the main test set, the IA-GTPF method demonstrated the following metrics for a 15-min forecast horizon: a Mean Absolute Error (MAE) of 0.9824 kW, a Root Mean Square Error (RMSE) of 2.5408 kW, and a Coefficient of Determination (R²) of 0.98947. For the 60-min horizon, the corresponding values were 1.3940 kW, 4.2017 kW, and 0.97122. The QuantileForest model showed a lower MAE for the 15-min horizon (0.9695 kW); however, IA-GTPF achieved the lowest RMSE and highest R² values. For the 60-min horizon, the IA-GTPF method demonstrated the lowest MAE and RMSE values among all evaluated models.