# TGN: A Temporal Graph Network for Physics Prediction
## 2 Related Work  
The development and execution of simulations for complex physical systems can be highly time consuming, and modeling complex physical problems using machine learning models has become an important area of research. Learnable models are useful for accelerating simulations of aerodynamics [1] or turbulence [21; 22] and have achieved superior performance in tasks such as weather prediction [23] and graphical visualization [24]. Several studies have introduced physical expertise by incorporating loss terms [25] or feature normalization based on physical information [2] to enhance prediction accuracy. Most of these approaches utilize convolutional neural networks on regular meshes, which are widely employed for learning complex physical systems. However, there has been a recent surge of interest in leveraging GNNs for learnable simulators. GNNs offer the capability to simulate on meshes with irregular or adaptive resolutions. For instance, [PERSON] et al. [26] embedded an aerodynamic solver within a graph convolution architecture [27] to achieve super-resolution predictions. [PERSON] et al. [28] employed graph element networks to make predictions on 2D grid domains, whereas MeshGraphNets [3] extended GNN-based predictions to complex 3D systems with thousands of nodes.  
These methods can be categorized as either steady-state or next-step prediction models. However, next-step models often suffer from drift and error accumulation in the face of LTSF tasks due to the lack of information about historical time series. In contrast, sequence models can prevent error accumulation by modeling historical time series. Recently, Transformer-based solutions for LTSF tasks have proliferated and have been successfully applied to predict simple small physical systems [19]. However, when predicting complex large physical systems, graph coarsening [28; 29; 30] is required due to its high memory overhead, which can lead to higher errors in the first few steps of prediction [20]. [PERSON] et al. [18] introduced a set of simple single-layer linear models (LTSF-Linear), which significantly outperforms the Transformer-based complex LTSF models in experimental results under direct multi-step (DMS) prediction [31]. However, linear models cannot directly deal with unstructured data such as scale-varying meshes, and only take into account temporal features and ignore spatial dependence, making the predicted system dynamics unconstrained by physical space, so applying linear models to predict complex physical systems remains a challenge.  
In the field of traffic prediction, much research [32; 33; 34; 35; 36; 37] makes full use of spatiotemporal dependence to solve traffic prediction problems. Since these methods are based on CNNs to model spatial dependence, they are only applicable to Euclidean spaces, such as images or regular meshes, and cannot be extended to traffic networks with complex topology. In recent years, with the development of GNNs, a series of studies have extended traffic prediction to graph-structured data. [PERSON] et al. [38] proposed the DCRNN model, which introduces GNNs to model temporal dependence. [PERSON] et al. [39] proposed the A3T-GCN model to capture global time dynamics and spatial features. The model utilizes gated recurrent units (GRUs) [40] and graph convolution (GCN) to model the spatiotemporal dependence of traffic flow, and introduces an attention mechanism to focus on the global time information to improve prediction accuracy. Although these methods take into account spatiotemporal dependence and have achieved great success in traffic prediction tasks, they are inherently applicable to small 2D systems based on urban road networks and have limitations for complex high-dimensional physical systems.  
Based on this background, this paper develops a new neural network method for the spatiotemporal dependence of physical systems that can extend spatiotemporal modeling to complex physical systems with thousands of nodes.