A Novel Graph Neural Network for Zone-Level Urban-Scale Building Energy Use Estimation

Data-driven UBEM have gained popularity since model development requires less laborious processes and benefit from the use of smart sensors and data mining approaches [17]. They provide important insights into the energy consumption patterns of buildings in urban areas by analysing building stock and developing strategies to reduce energy consumption. Data-driven UBEM can be grouped as statistical models and machine learning (ML) models [25]. Statistical models utilise explicit mathematical functions to forecast building energy consumption based on input data [22]. ML models, on the other hand, learn from existing data a mapping to estimate building energy consumption [27]. random forest (RF), support vector machines (SVMs) and artificial neural networks (ANNs) are the most common ML algorithms. Many surveys (e.g., [4, 27, 35] and [18]) reviewed existing studies that use machine learning models in prediction of building energy consumption.

Nevertheless, the majority of data-driven UBEMs capture results based on the building level features, assuming that buildings are independent of one another. A prominent solution is to use graph neural networks (GNNs), which are deep learning algorithms based on graph representations that can model a set of objects and their relationships [37]. GNNs can use node and edge features to describe the relationships between buildings or zones. The representation of each node in a graph network is automatically defined by its attributes and the aggregate of the surrounding nodes because GNNs use a message passing mechanism [37]. Edges can be used to indicate the relationships between the interconnected buildings or zones, while nodes can be used to represent the particular building features, such as thermal characteristics, occupant behaviour, and internal loads. GNN models may learn about a building's energy consumption based on its own characteristics and propagate the energy impact of nearby buildings via graph structure by information propagation [17].

Hu et al. [17] proposed a spatio-temporal GNN model to predict hourly energy consumption of buildings based on graph representation. Their study considered solar-based inter-dependencies between 26 buildings. They concluded that graph-based data-driven models can greatly reduce building energy usage on an urban scale by comparing the performance of the proposed model with other time-series machine learning models. Lu et al. [21] developed a GNN model to learn the energy load patterns of each basic block. After applying their methodology on 800 buildings and comparing different data-driven models (ANNs, support vector regression (SVR), random forest (RF), and gradient boosting tree), their results indicated that the proposed GNN showed the highest performance accuracy. Chen et al. [9] developed a GNN-based cooling load prediction method. They compared the results with onsite data, concluding that the proposed GNN model is effective in cooling load prediction.

As reviewed above, we note that recent studies [9, 17, 21], have started exploring the use of GNN for UBEM, demonstrating the promise of representing relations among entities for UBEM. Differently from these studies:

• Existing approaches consider zones in isolation, ignoring the heat transfer between neighboring zones through shared internal surfaces. Especially when the indoor conditions (internal loads, set points, schedules) of neighboring zones are sufficiently different from one another, heat transfer between zones can constitute a significant portion of the total heat gains and losses.
  
• For more accurate estimation of energy use, we utilize GNNs that incorporate zone-level inter-dependencies. To be able to integrate zone-level inter-dependencies, our approach extends a GNN by taking into account the inter-dependency representations while making predictions.
  
• Prior GNN-based studies considered only small-scale neighborhoods with small number of zones such as 800 buildings with 4 to 7 zones per building in (Lu et al. [21]) whereas we validated our approach on an urban-scale with 5866 buildings with 64462 zones.
  

Modeling zone inter-dependencies is an integral component of our contribution and has an effect on capturing heat transfer between neighboring zones. While representing relations between neighboring zones, we use the U value and the area of the wall connecting the zones as well as the floor difference between the zones. Using these parameters and features representing the zones, we model each building as homogeneous bidirectional graphs. Each node represents a zone and each bidirectional edge represents relations between neighboring zones.

UBEM requires geometric data and semantic data for the buildings in the neighbourhood. Geometric data includes physical characteristics as floor height, number of floors, building footprint, orientation, building dimensions, and local site conditions. Semantic data includes building function, construction year, construction material properties, internal loads, HVAC properties, setpoints and occupancy patterns.

Geometric data was procured from different sources. Building footprints were gathered from the Çankaya municipality. Data on the number of floors, units, and their functionalities were gathered from the Ministry of Interior, General Directorate of Population and Citizenship Affairs [32]. Semantic data, on the other hand, were acquired from the Energy Performance Certificates (EPC) by the Turkish Ministry of Urbanization and Climate Change [10], which includes data on year of construction, and construction materials.

Each building and its residential units were simulated sequentially in an automated process. In parallel, each zone's attributes (which will be mostly used for GNN model training) were recorded in the UBEM dataset. During each simulation, the associated building semantic data was retrieved from the database. Subsequently, simulation results were tagged with the building's block and parcel numbers and logged in the same dataset.

In preparation of the UBEM datasets for missing data and data generation steps, two key density estimation techniques, namely parametric (PDE) and non-parametric (NPDE), are employed. Parametric Density Estimation (PDE) assumes that the density is represented by a known parametric family of distributions (e.g., normal or uniform distribution) with unknown parameters, where the missingness is equal to 100%, whereas Non-Parametric Distribution (NPDE) requires sampling from the associated distribution to generate the density function; it can be applied to data sets with $0 < missingness < 100\%$. When the missingness of the data is greater than zero, we reproduced the missing data using EPCs with non-parametric distribution and assigned them to the buildings that have no data (data imputation). These data include UWall, URoof, UGround, UWindow, WWR and Qpeople. In the study, data on occupants (except for person density), SHGC, COPBoiler, and infiltration rate were completely missing. For these data, we generated new data based on PDE using uniform distribution (data generation). Table 1 shows the statistics of dataset based on data imputation and generation.

We made our simulations using EnergyPlus 9.2 with real data calibration. Heating energy demand (Q_H) is calculated as a performance objective as the heating load is predominate in Ankara. Figure 3 and Table 2 show the distribution and statistics of Q_H. The mean of Heating End Use is calculated as 79.02 Kwh/m² and while standard deviation is calculated as 49.02. The Heating End Use ranges between 1.591 and 371.769 Kwh/m².

To predict heating demand for buildings, we used the final node feature representations produced by GNN model as an input to the MLP. In this setting, GNN acts as the “feature extractor” and MLP makes predictions on the final representations of the node features. MLP has four layers with ReLU [24] activation while GNN has Leaky ReLU [23] activation functions. We use L2 normalisation between every GCN layer and layer normalisation between every GCN layer and every MLP layer[5].

To get the best results, we made an extensive hyperparameter search for the number of GNN layers, the number of layers in the message function (Ψ), the output shape of the message function (embedding size), the aggregator type, the dynamic attention use, learning rate and batch size. We trained our models with the ADAM optimizer [19].

The dataset is split into three parts for training, validation and testing. Each part consists of 70, 15 and 15 percent of the dataset respectively.

We use the commonly-used R² score and Root Mean Squared Error (RMSE) as performance metrics.

We selected MLP, GraphSAGE [14], GCN [20] and GAT [6] as baseline models. All these models use only node (zone) features and do not consider inter-dependencies (edge features) between zones.

For a fair comparison, we trained the baseline models by performing a hyperparameter search with parameters listed in Table 3. For MLP, we used ReLU [24] non-linearity, as it performed better. For GNN baselines, we used the final representations of the nodes as input for their MLP predictors.

We predicted heating load using the setup from the previous section and compared our model with the baseline models described in Section 5.2. Note that the baseline models also work at the zone-level but do not take into account features (discussed in Section 3.1) between the neighboring zones.

The quantitative results of all methods are provided in Table 4. The R² scores and RMSE values in the table suggest that our approach (GUBEM) provides the best values compared to not only MLP but also other GNN-based approaches. Considering that the baseline GNN approaches are also zone-based, the performance of GUBEM acknowledges the importance of capturing the inter-dependence between zones with explicit features.

We also compared the performances of the methods by plotting the predictions with respect to the ground truth values. The plots in Figure 4 show that our model generalizes better than the baseline models. We argue that our model's ability to use inter-zone relations with its message passing mechanism yields higher performance in node-level prediction.