A Hydraulically Informed ANN Surrogate Framework for Nonlinear Open-Channel Flow Analysis

Open-channel hydraulic analysis often requires repeated solution of implicit nonlinear equations and numerical integration of gradually varied flow (GVF), which can become computationally demanding in inverse, optimization, and sensitivity applications. This study develops a hydraulically informed artificial neural network (ANN) surrogate framework comprising ten independently trained models for normal and critical depths, alternative and conjugate depths, GVF-related water-surface behavior, and profile-based discharge inference. Hydraulic information is introduced through physically meaningful, and where appropriate dimensionless, variables and reference solutions derived from established governing equations or numerical hydraulic models, while ANN optimization remains data driven. Equation-generated test sets quantified surrogate fidelity, whereas HEC-RAS comparisons were treated as numerical hydraulic cross-verification rather than independent physical validation. The forward surrogates reproduced their reference mappings with high accuracy within the represented domains. Benchmarking against Random Forest, support vector regression, and Gaussian Process Regression for Models 1, 5, and 7 showed no universal algorithmic superiority; however, ANN provided a favorable trade-off among accuracy, relative-error robustness, compactness, and repeated-inference efficiency. For Model 7, ANN inference was approximately 249 times faster than conventional GVF calculation, with development cost recovered after about 1.03 × 105 evaluations. Model 9 inferred discharge with a 4.75% error in the profile-based test. Observation-based assessment using 16 historical Missouri River stage–discharge events showed that direct HEC-RAS inversion yielded a MAPE of 44.71%, whereas observation-only ANN and hybrid HEC-RAS-ANN discrepancy correction reduced MAPE to 10.25% and 9.83%, respectively. The framework is therefore a computational complement to established hydraulic equations and numerical models, with broader field validation and explicit uncertainty treatment required for general deployment.