Precipitation modeling in Northeastern Bangladesh–India transboundary flood regions using bi-metaheuristic-optimized NMF-neural network

Two fundamental questions in rainfall modeling using Artificial Neural Networks (ANN) are: (1) how to best handle highly nonlinear, noisy, short-duration rainfall data, and (2) how to locate a solution to the optimization issue of ANN, particularly in formulating the optimum weights and biases. Most of the single-step rainfall forecasting models that rely on single-step optimization and conventional ANN feature selection techniques are not capable of adequately addressing these critical challenges. In this study, Non-Negative Matrix Factorization (NMF) is applied to model complex short-term rainfall patterns, and an optimal differential approach is used to compute NMF components. For the optimization of the ANN model, in this paper, three recently proposed metaheuristic algorithms namely Harris Hawks Optimization (HHO), Egret Swarm Optimization Algorithm (ESOA), and Hippopotamus Optimization (HO) are explored along with traditional well-known methods like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Furthermore, a two-step hybrid optimization approach is introduced to enhance ANN performance in rainfall forecasting. This significantly improves model precision, with reductions in mean squared error (MSE) ranging from 1.00% to 97.46% in Sylhet, 8.33% to 97.10% in Chittagong, 6.96% to 89.57% in Meghalaya, and 17.74% to 76.09% in Assam compared to single-step optimization models. The results indicate that the two-step optimization approach not only outperforms single optimization techniques but also outperforms recently introduced metaheuristic algorithms such as HHO, ESOA, and HO, demonstrating its superior potential for improving the accuracy of rainfall modeling. On the other hand, the sensitivity analysis of the hidden neuron indicates that the impact of hidden neuron quantity is highly sensitive to the optimizer and the characteristics of the data.