ЗАДАЧІ МАТЕМАТИЧНОГО МОДЕЛЮВАННЯ КОЕФІЦІЄНТА ГІДРАВЛІЧНОГО ОПОРУ НА ОСНОВІ НЕЙРОННИХ МЕРЕЖ

The paper addresses a suite of mathematical-modelling tasks for estimating the Chézy hydraulic resistance coefficient in river flows using artificial neural networks (ANNs). A critical review of 43 classical and contemporary empirical and semi-empirical equations—systematised into four groups according to the dominant factors of hydraulic resistance—shows that none provides universally reliable accuracy owing to seasonal variability of channel conditions, spatio-temporal differences in hydromorphological parameters, and measurement uncertainty in the field. To overcome these limitations, we propose a computational model based on a fully connected feed-forward ANN with one hidden layer that approximates the continuous functional relationship between the Chézy coefficient and six governing parameters: Manning’s coefficient, water-surface slope, mean flow width and depth, roughness-element height, and hydraulic radius. Rules for constructing training and testing datasets are developed to handle gaps, anomalies, and collinearity in the data. Model validation on ten reaches of lowland rivers (Dnipro, Desna, Prypiat) and six reaches of mountain rivers (Tysa, Teresva, Latorytsia, Opir, Rika, Chornyi Cheremosh) yielded a Nash–Sutcliffe efficiency of NSE = 0.94–0.98 and a relative discharge-prediction error of 0.9–13.9 %. To enhance forecast robustness, an ensemble scheme of three ANNs trained via bagging is proposed; it reduced the error to 0.3–6.1 % and raised NSE to 0.991–0.998. The results confirm the high predictive capability of the approach and its suitability for rapid assessment of hydraulic resistance under limited input information—crucial for hydraulic-structure design, flood-risk management, and sustainable water use amid climate change. Implementation of the algorithm in Python facilitates integration with hydrological IT systems and practical deployment.