Stefanyshyn, DmytroKhodnevych, YaroslavTrofymchuk, OleksandrKorbutiak, VasylBenatov, Daniel2026-03-122026-03-122025Mathematical modelling tasks for hydraulic resistance coefficient estimation using neural networks / Dmytro Stefanyshyn, Yaroslav Khodnevych, Oleksandr Trofymchuk, Vasyl Korbutiak, Daniel Benatov // Матеріали XХV Міжнародної науково-практичної конференції «Екологія. Людина. Суспільство» пам’яті д-ра Дмитра СТЕФАНИШИНА (12 червня 2025 р., м. Київ, Україна). – Київ : КПІ ім. Ігоря Сікорського, 2025. – С. 293-299. – Бібліогр.: 6 назв.2710-3315 (Online)https://ela.kpi.ua/handle/123456789/79466This paper presents a comprehensive approach to estimating the Chézy roughness coefficient as a key parameter of hydraulic resistance in natural river channels. Based on the analysis of 43 wellknown empirical and semi-empirical formulae for C, as well as 13 formulae for the Gauckler–Manning coefficient, the dependencies were systematised and classified into groups according to hydromorphological and hydraulic parameters. An artificial neural network (ANN) was developed to estimate the coefficient C considering key hydromorphological factors. The model was validated using data from the Dnipro, Desna, and Prypiat rivers; the Nash–Sutcliffe Efficiency (NSE) values ranged from 0.94 to 0.98, with relative errors of 0.9–13.9%. Additional testing was conducted on mountain rivers (Tysa, Teresva, Latorytsia, Opir, Rika, Chornyi Cheremosh), where anomalous values were excluded from the training datasets, improving prediction accuracy. It was demonstrated that the use of one- or two-layer ANNs is appropriate when high-quality training data are available. To improve accuracy under limited data conditions, an ensemble model (ANN-A, ANN-B1, ANNB2) was implemented using the bagging method. A strategy of independent training of networks was applied, followed by aggregation of outputs using majority voting. The testing results showed relative discharge errors ranging from 0.3% to 6.1%, and NSE values from 0.991 to 0.998. The study confirms the high accuracy and practical applicability of the ensemble approach for estimating the Chézy coefficient in contexts with limited hydromorphological information.enChézy coefficienthydraulic resistanceartificial neural networksmodel ensemblemathematical modellingriver flowshydromorphologyNSEmachine learninghydraulic engineering structuresкоефіцієнт Шезігідравлічний опірштучні нейронні мережіансамбль моделейматематичне моделюваннярічкові течіїгідроморфологіямашинне навчаннягідротехнічні спорудиArticleС. 293-299https://doi.org/10.20535/EHS2710-3315.2025.3323580000-0002-7620-16130000-0002-5510-11540000-0003-3358-62740000-0002-8273-23060000-0001-9626-6759