PSO-Optimized Hybrid ARIMA-LSTM for Provincial Water Forecasting
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Accurate macro-administrative water distribution forecasting is essential for infrastructure planning and regional governance. While most prior studies focus on short-term urban demand, provincial-scale systems exhibit aggregated heterogeneity, structural shifts, and limited annual observations that challenge conventional forecasting approaches. This study proposes a Particle Swarm Optimization (PSO)-optimized hybrid ARIMA-LSTM framework designed for cross-domain robustness in macro-scale infrastructure forecasting. Linear components are modeled using ARIMA, nonlinear residuals are learned via LSTM, and PSO jointly optimizes statistical and neural hyperparameters under validation constraints. The framework is evaluated across 34 Indonesian provinces using sequential train–validation–test splits and recursive multi-step forecasting. Beyond conventional accuracy metrics (RMSE, MAE, MAPE, R²), this study introduces cross-provincial RMSE variance and multi-domain Diebold-Mariano statistical testing as robustness indicators. Results show that the PSO-optimized hybrid model achieves the lowest average MAPE (21.79%), reduces inter-provincial RMSE variance by approximately 15%, dominates in 52.9% of provinces, and demonstrates statistically significant improvement in 76.5% of provinces. These findings confirm that optimization-enhanced hybrid decomposition improves structural stability and cross-domain generalization in heterogeneous macro-administrative infrastructure systems.
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[1] Tareq, M. F., Mels, A., Radjkoemar, R., Kujawa-Roeleveld, K., & Haldar, K. (2026). Scenario-based drinking water demand forecasting under climate change uncertainties: a study on Dhaka City, Bangladesh. Science of the Total Environment, 1012. doi:10.1016/j.scitotenv.2025.181198.
[2] Capone, J. A., & Marston, L. T. (2025). Water Demand Projection Accuracy and Demand Management Trends in California Cities. Water Resources Research, 61(11), e2025WR040474. doi:10.1029/2025WR040474.
[3] Ye, J., Meng, X., Wang, H., Zhou, Q., An, S., An, T., Ghorbani Bam, P., & Rosso, D. (2025). ARIMA-Based Forecasting of Wastewater Flow Across Short to Long Time Horizons. Mathematics, 13(13), 2098. doi:10.3390/math13132098.
[4] Tran, T. D., & Kim, J. (2024). Guidance on the construction and selection of relatively simple to complex data-driven models for multi-task streamflow forecasting. Stochastic Environmental Research and Risk Assessment, 38(9), 3657–3675. doi:10.1007/s00477-024-02776-2.
[5] Pashaei, E., Sürücü, D., Sakal, E., & Korkmaz, A. N. (2025). An Ensemble-Based Approach for Water Demand Prediction: Comparative Analysis of Conventional, Machine Learning, and Deep Learning Techniques. Turkish Journal of Mathematics and Computer Science, 17(2), 338–365. doi:10.47000/tjmcs.1723524.
[6] Estrada, A. V., Henning, E., Kalbusch, A., & Walter, O. M. F. C. (2025). Urban water demand forecasting via artificial neural network models: a case study in Southern Brazil. Discover Sustainability, 6(1), 1105. doi:10.1007/s43621-025-01917-z.
[7] Iranmehr, S., Moosavi, A., & Kazemzadeh Hannani, S. (2026). Improving short-term water demand forecasting with development of dynamic neural network models considering environmental and sociocultural features. International Journal of Environmental Science and Technology, 23(4), 283. doi:10.1007/s13762-025-06995-0.
[8] Yuan, R., Man, Y., Su, K., Zhou, X., & Liu, S. (2026). Improving multi-step water demand forecasting performance: Static, past, future, and periodic feature importance. Journal of Water Process Engineering, 83. doi:10.1016/j.jwpe.2026.109679.
[9] Liu, B., Li, J., Jiang, X., Gibbs, M., Zhu, Z., Wang, X., Joehnk, K., & Gao, L. (2026). Enhancing riverine cyanobacterial bloom prediction: A hybrid deep learning approach combining wavelet decomposition, double-layer LSTM, ARIMA, and residual compensation. Environmental Modelling and Software, 196. doi:10.1016/j.envsoft.2025.106764.
[10] Sheikh Khozani, Z., Barzegari Banadkooki, F., Ehteram, M., Najah Ahmed, A., & El-Shafie, A. (2022). Combining autoregressive integrated moving average with Long Short-Term Memory neural network and optimisation algorithms for predicting ground water level. Journal of Cleaner Production, 348. doi:10.1016/j.jclepro.2022.131224.
[11] Wang, T., Chen, W., & Tang, B. (2024). Water quality prediction using ARIMA-SSA-LSTM combination model. Water Supply, 24(4), 1282–1297. doi:10.2166/ws.2024.060.
[12] Kilinc, H. C. (2022). Daily Streamflow Forecasting Based on the Hybrid Particle Swarm Optimization and Long Short-Term Memory Model in the Orontes Basin. Water (Switzerland), 14(3), 490. doi:10.3390/w14030490.
[13] Pranolo, A., Mao, Y., Wibawa, A. P., Utama, A. B. P., & Dwiyanto, F. A. (2022). Robust LSTM With Tuned-PSO and Bifold-Attention Mechanism for Analyzing Multivariate Time-Series. IEEE Access, 10, 78423–78434. doi:10.1109/ACCESS.2022.3193643.
[14] Yue, H., Wang, Y., Zhang, L., & Yang, T. (2025). A machine learning-based water supply forecasting model to quantify the impact of snow water equivalent on seasonal streamflow variability over the western U.S. Journal of Hydrology, 660. doi:10.1016/j.jhydrol.2025.133465.
[15] Hochreiter, S., & Schmidhuber, J. (1997). Long Short-Term Memory. Neural Computation, 9(8), 1735–1780. doi:10.1162/neco.1997.9.8.1735.
[16] Velayudhan, N. K., Devidas, A. R., & Savić, D. (2025). Generative AI for spatio-temporal multivariate imputation and demand prediction in water distribution systems. Results in Engineering, 27. doi:10.1016/j.rineng.2025.106178.
[17] Maußner, C., Oberascher, M., Autengruber, A., Kahl, A., & Sitzenfrei, R. (2025). Explainable artificial intelligence for reliable water demand forecasting to increase trust in predictions. Water Research, 268. doi:10.1016/j.watres.2024.122779.
[18] Gil-Gamboa, A., Torres, J. F., Martínez-Álvarez, F., & Troncoso, A. (2025). Energy-efficient transfer learning for water consumption forecasting. Sustainable Computing: Informatics and Systems, 46. doi:10.1016/j.suscom.2025.101130.
[19] Huang, H., Que, G., & Wu, M. (2025). A simple and high-accuracy method for minute-level water demand forecasting in district metering areas. Journal of Hydrology, 652. doi:10.1016/j.jhydrol.2025.132698.
[20] Lin, P., Zhang, X., Gong, L., Lin, J., Zhang, J., & Cheng, S. (2025). Multi-timescale short-term urban water demand forecasting based on an improved PatchTST model. Journal of Hydrology, 651. doi:10.1016/j.jhydrol.2024.132599.
[21] Samih, I., & Loudyi, D. (2025). Predicting Monthly Urban Water Demand in a Changing Climate: a Case Study of Casablanca City, Morocco. Water Conservation and Management, 9(1), 113–119. doi:10.26480/wcm.01.2025.113.119.
[22] Hao, W., Cominola, A., & Castelletti, A. (2024). Combining wavelet-enhanced feature selection and deep learning techniques for multi-step forecasting of urban water demand. Environmental Research: Infrastructure and Sustainability, 4(3), 035005. doi:10.1088/2634-4505/ad5e1d.
[23] Hao, W., Cominola, A., & Castelletti, A. (2025). Short-Term Memory and Regional Climate Drive City-Scale Water Demand in the Contiguous US. Earth’s Future, 13(1), 035005. doi:10.1029/2024EF004415.
[24] Zhang, Y., Li, J., Sun, S., Li, G., Yang, Q., Sun, Y., Wang, X., & Xu, C. (2024). Short-Term Water Supply Forecasting for Water Treatment Plant Using Temporal Multi-Scale Features. Water (Switzerland), 16(24), 3573. doi:10.3390/w16243573.
[25] Alvisi, S., Franchini, M., Marsili, V., Mazzoni, F., Salomons, E., Housh, M., Abokifa, A., Arsova, K., Ayyash, F., Bae, H., Barreira, R., Basto, L., Bayer, S., Berglund, E. Z., Biondi, D., Boloukasli Ahmadgourabi, F., Brentan, B., Caetano, J., Campos, F., … Zou, J. (2025). Battle of Water Demand Forecasting. Journal of Water Resources Planning and Management, 151(10), 04025049. doi:10.1061/jwrmd5.wreng-6887.
[26] Muñoz-Rodríguez, D., González-Ortega, M. J., Aguilera-Ureña, M. J., Ortega-Ballesteros, A., & Perea-Moreno, A. J. (2025). Innovation ARIMA models application to predict pressure variations in water supply networks with open-loop control. Case study in Noja (Cantabria, Spain). Energy Nexus, 18. doi:10.1016/j.nexus.2025.100423.
[27] Uzlu, E., & Dede, T. (2025). Development of hybrid models to forecast water demand in the city of Ankara. Soft Computing, 29(17–18), 5401–5414. doi:10.1007/s00500-025-10904-5.
[28] Harvey, D., Leybourne, S., & Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13(2), 281–291. doi:10.1016/S0169-2070(96)00719-4.
[29] Wang, K., Xie, X., Liu, B., Yu, J., & Wang, Z. (2024). Reliable multi-horizon water demand forecasting model: A temporal deep learning approach. Sustainable Cities and Society, 112. doi:10.1016/j.scs.2024.105595.
[30] Jiang, Q., Guo, W., Wang, Z., Wu, Y., Zhao, Y., Tao, M., & Sun, Y. (2024). Forecasting regional water demand using multi-fidelity data and harris hawks optimization of generalized regression neural network models – A case study of Heilongjiang Province, China. Journal of Hydrology, 634. doi:10.1016/j.jhydrol.2024.131084.
[31] Namdari, H., Ashrafi, S. M., & Haghighi, A. (2024). Deep learning-based short-term water demand forecasting in urban areas: A hybrid multichannel model. Aqua Water Infrastructure, Ecosystems and Society, 73(3), 380–395. doi:10.2166/aqua.2024.200.
[32] Dang, C., Zhang, H., Yao, C., Mu, D., Lyu, F., Zhang, Y., & Zhang, S. (2024). IWRAM: A hybrid model for irrigation water demand forecasting to quantify the impacts of climate change. Agricultural Water Management, 291. doi:10.1016/j.agwat.2023.108643.
[33] Diebold, F. X., & Mariano, R. S. (1995). Comparing Predictive Accuracy. Journal of Business & Economic Statistics, 13(3), 253. doi:10.2307/1392185.
[34] Pesantez, J. E., González, L., & Li, B. (2025). Exploring the predictive capabilities of neural networks and state space models on hourly water demand forecasting. Journal of Hydrology, 662. doi:10.1016/j.jhydrol.2025.133317.
[35] Pu, Z., Han, D., Yan, H., Tao, T., & Xin, K. (2024). Enhancing accuracy and interpretability of multi-steps water demand prediction through prior knowledge integration in neural network architecture. Water Research X, 24, 100247. doi:10.1016/j.wroa.2024.100247.
[36] Pernat, M. R., Kasprzyk, J., Zagona, E., Walker, S. D., & Livneh, B. (2025). The relative importance of model type and input features for water supply forecasting in snow-dominated basins of the southwestern US. Journal of Hydrology: Regional Studies, 60. doi:10.1016/j.ejrh.2025.102548.
[37] Mohammadi, M., Gato-Trinidad, S., & Kuok, K. K. (2024). The limitation of machine learning methods for water supply and demand forecasting: A case study for Greater Melbourne, Australia. Water Supply, 24(11), 3848–3861. doi:10.2166/ws.2024.225.
[38] Liu, H., Xing, R., & Davies, E. G. R. (2025). Forecasting municipal water demands: Evaluating the impacts of population growth, climate change, and conservation policies on water end-use. Sustainable Cities and Society, 130. doi:10.1016/j.scs.2025.106581.
[39] Xu, A., Zhang, T., Zhang, X., Shao, Y., Yu, T., Chu, S., & Qian, L. (2026). Multi-scale Spatio-temporal graph neural network for enhanced water demand forecasting. Water Research, 288. doi:10.1016/j.watres.2025.124711.
[40] Homaei, M., Tarif, M., Rodríguez, P. G., Ávila, M., & Caro, A. (2026). Adaptive multi-domain uncertainty quantification for digital twin water forecasting. Machine Learning with Applications, 23, 100812. doi:10.1016/j.mlwa.2025.100812.
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