Optimizing deep neural networks for estimating soil water retention curves: A comparison of metaheuristic and numerical algorithms

Abstract Accurate representation of the soil water retention curve (SWRC) is essential in hydrological modeling, particularly for predicting unsaturated zone dynamics in water and solute transport. Choosing an effective optimization method for deep neural network training significantly influences algorithm convergence and accuracy in modeling soil–water dynamics. In this study, two metaheuristic techniques including particle swarm optimization (PSO) and ant colony optimization (ACO) were compared to the Levenberg–Marquardt (LM) numerical method for optimizing a deep feedforward neural network (DFNN) in the SWRC estimation, which has not been previously implemented. In this regard, the effectiveness of three optimization methods was evaluated using seven pedotransfer functions (PTFs) to predict the parameters of the Brutsaert model for 354 soil samples from the UNsaturated SOil hydraulic DAtabase (UNSODA). The PTFs were developed with various input variables including clay, sand, particle diameters ( d 30 and d 50), bulk density (BD), field capacity moisture content (FCMC), and wilting point moisture content (WPMC). Test results revealed that the LM method had a higher average reliability compared to the ACO and PSO methods by 38.46% and 6.18%, respectively, in terms of the integral root mean square error (IRMSE). PTF7 ( d 30 + d 50 + BD + FCMC + WPMC) achieved the best performance under LM, with IRMSE = 0.030 and 0.044 cm 3 cm −3 , and R 2 = 0.993 and 0.981 at the training and testing data, respectively. Compared to other optimization techniques in neural networks, this study demonstrates that the LM method in DFNN is highly effective for hydrological modeling. LM enhances convergence reliability, reduces trapping in local minima, and improves deep network capacity for capturing complex data patterns.