Transformer Networks and Loss with Punishment for Optimized Management of Urban Water Supply System

Accurate water demand forecasting is critical for the
efficient
operation and management of water supply systems, traditional forecasting
models often show limited performance, with errors equally 50%/50%
split between underestimation and overestimation. Here we show a model
based on transformer (TF) to predict water demand quantity, comparing
its performance with statistical models, recurrent neural network
(RNN), long short-term memory (LSTM). To tackle the critical issue
of underestimating water demand, we design a penalized loss function
that constrains the model’s output distribution when predicting
anomalies, drawing inspiration from the Chinese saying “killing
the chicken to scare the monkey.” The rationale for this penalized
loss function is explained through the principles of the transformer
network and loss function with punishment (TFP) model and interpretability
analysis. If actually deployed, the TFP model would reduce water supply
by 8.97%, achieving a mean absolute percentage error of 2.93% and
an underestimation probability of just 30.63%. Additionally, we outline
a process for applying the penalized loss function to tackle a broader
range of environmental challenges, with the goal of addressing more
diverse environmental issues in the future.