Water is one of the most important resources for economic and social developments. Daily water demand
forecasting is an effective measure for scheduling urban water facilities. This work proposes a multi-scale
relevance vector regression (MSRVR) approach to forecast daily urban water demand. The approach uses
the stationary wavelet transform to decompose historical time series of daily water supplies into different
scales. At each scale, the wavelet coefficients are used to train a machine-learning model using the
relevance vector regression (RVR) method. The estimated coefficients of the RVR outputs for all of the
scales are employed to reconstruct the forecasting result through the inverse wavelet transform. To better
facilitate the MSRVR forecasting, the chaos features of the daily water supply series are analyzed to
determine the input variables of the RVR model. In addition, an adaptive chaos particle swarm optimization
algorithm is used to find the optimal combination of the RVR model parameters. The MSRVR
approach is evaluated using real data collected from two waterworks and is compared with recently
reported methods. The results show that the proposed MSRVR method can forecast daily urban water
demand much more precisely in terms of the normalized root-mean-square error, correlation coefficient,
and mean absolute percentage error criteria.