The relationship between urban water and energy demand is crucial for resource efficiency, sustainability, and environmental conservation. Rapid urbanization, population growth, and climate change necessitate integrated models that capture the complex interdependencies, feedback loops, and trade-offs between water and energy systems. This research addresses this intricate relationship by developing a modified Rotor Hopfield Neural Network (RHNN) Model using input indicators like population data, GDP, water consumption, precipitation, electricity consumption, wastewater discharge, and industrial coal usage. The model is optimized using a modified metaheuristic, called Contracted Thermal Exchange Optimizer (CTEO), resulting in a comprehensive forecast of urban water-energy demand. The model's superior efficiency is demonstrated by comparing it with other contemporary methods. Upon comparison with alternative approaches, it is clear that the RHNN/CTEO model surpasses them, showcasing a mean relative error of 1.47% for water usage and 2.60% for energy consumption. This leads to an overall average MRE of 2.03%. This research contributes to the existing body of knowledge by offering an advanced model for urban water-energy demand forecasting, providing valuable insights for policymakers, urban planners, and stakeholders in making informed decisions related to resource allocation, infrastructure development, and sustainable urban development.

Advancing urban water-energy demand predictions with a rotor hopfield neural network model optimized by contracted thermal exchange optimizer