Water-energy nexus has been a popular topic of rese arch in recent years. The relationships between the demand for water resources and energy are intense and closely connected in urban areas. The primary, secondary, and tertiary industry gross domestic product (GDP), the total population, the urban population, annual precipitation, agricultural and industrial water consumption, tap water supply, the total discharge of industrial wastewater, the daily sewage treatment capacity, total and domestic electricity consumption, and the consumption of coal in industrial enterprises above the designed size were chosen as input indicators. A feedforward artificial neural network model (ANN) based on a back-propagation algorithm with two hidden layers was constructed to combine urban water resources with energy demand. This model used historical data from 1991 to 2016 from Wuxi City, eastern China. Furthermore, a multiple linear regression model (MLR) was introduced for comparison with the ANN. The results show the following: (a) The mean relative error values of the forecast and historical urban water-energy demands are 1.58 % and 2.71%, respectively; (b) The predicted water-energy demand value for 2020 is 4.843 billion cubic meters and 47.561 million tons of standard coal equivalent; (c) The predicted water-energy demand value in the year 2030 is 5.887 billion cubic meters and 60.355 million tons of standard coal equivalent; (d) Compared with the MLR, the ANN performed better in fitting training data, which achieved a more satisfactory accuracy and may provide a reference for urban water-energy supply planning decisions.

Considering the issues of water scarcity, water environment deterioration, and unreasonable allocation of water resources in the urban area of the Yellow River Basin, this paper introduces the human–water harmony theory to the allocation of regional water resources. Based on an analysis of the structural characteristics of the regional water resource system, the harmonious water resource allocation (HWRA) model—which includes three sub-systems (i.e., the water service system, ecological environmental system, and economic and social system)—is established. In addition, considering the uncertain factors in the HWRA model, the inexact fuzzy multi-objective programming (IFMOP) method is used to solve the model, aiming at achieving the minimum amount of regional water scarcity, the minimum amount of sewage discharge, and the maximum total economic benefit. A case study of water resource allocation of Binzhou, a city located in the Yellow River Basin, is conducted to validate the model. The model solution results show that the water resource system in Binzhou in 2025 and 2035 could be optimized after harmonious allocation, especially in terms of the water service and ecological environmental systems. Compared with the optimal water resource allocation (OWRA) model, the HWRA model has a more scientific water supply structure, and a smaller amount of sewage discharge. The HWRA model solves the variables using an interval number, so it can flexibly and scientifically reflect the decision-making process.