# A Heat Load Prediction Method for District Heating Systems Based on the AE-GWO-GRU Model
## 1 Introduction
### Related Works  
In the early stages of heat load prediction research, statistical analysis techniques were primarily used, leveraging statistical and mathematical expertise to construct prediction models. Their straightforward form offers significant advantages in modeling and prediction speed [6]. Some widely used statistical analysis prediction models include recursive least squares (RLSs) [7], multiple linear regression (MLR) [8], auto-regressive (AR) [9], autoregressive with extra inputs model (ARX) [10], autoregressive and moving average model (ARMA) [11], and autoregressive integrated moving average model (ARIMA) [12]. Despite their lower modeling complexity and shorter modeling times, these statistical models typically only consider time factors, neglecting other external elements that can influence the prediction model. Multi-dimensional heat load sequence data have nonlinear relationships that are difficult to capture, making these models less reliable in complex heat load prediction scenarios. With the rapid advancement of industrial hardware and artificial intelligence technology, models based on machine learning and deep learning have demonstrated significant capabilities for learning and mapping nonlinear objects, offering new potential for the development of heat load prediction. Examples of popular machine learning regression techniques include support vector regression (SVR) [13], decision tree (DT) [14], random forest (RF) [15], and neural network models [16]. [PERSON] et al. [17] developed a heat load prediction model for heating systems using a BP neural network by quantifying temperature and date types. The genetic algorithm optimized the neural network's connection weights and thresholds, resulting in accurate 24-h heat load predictions. [PERSON] et al. [18] determined the optimal parameters of the multilayer perceptron (MLP) through different optimization algorithms to establish a heat load prediction model. The RMSE, R2, and MAE of the MLP model optimized by the biogeography-based optimization algorithm are 2.82, 0.92, and 2.15, respectively. Despite their advantages of speed and high precision for small data sets, these traditional machine learning algorithms are ineffective for handling large-scale data sets and often neglect the feature expression of heat load data in time series. Figure 1: The change trend in urban district heating area from 2013 to 2022. Recurrent neural networks (RNNs) [19] have gained popularity in time series prediction due to their superior ability to remember historical data compared to other algorithms. Long short-term memory (LSTM) [20] introduces a gated unit structure based on RNNs, enabling it to learn sequence dependencies in prediction problems. The gated recurrent unit (GRU) [21] simplifies the LSTM model structure, ensuring prediction accuracy without overfitting and offering better adaptability. [PERSON] et al. [22] developed a GRU-based heat load prediction model that fully leverages GRU's ability to memorize long-term time series data, resulting in enhanced prediction accuracy. However, GRU networks that rely solely on empirical parameters can be more prone to randomness and may fall into local optima due to their complex parameters, potentially impacting final heat load prediction values. The grey wolf optimization (GWO) algorithm [23], a swarm intelligence optimization method that simulates the predation behavior of grey wolves, has been recently proposed. Its advantages include easy implementation, few parameters, and strong convergence. Compared to other popular algorithms such as particle swarm optimization (PSO) and genetic algorithm (GA) [24], the GWO algorithm offers higher convergence speed and superior search capabilities. Consequently, it is frequently employed in model parameter optimization and adjustment [25; 26]. The GRU model requires a substantial amount of data for training. Inadequate training data can lead to overfitting issues and reduce the model's accuracy. A common method to address this issue is data augmentation.