Bilateral Trade Flow Prediction by Gravity-informed Graph Auto-encoder
Naoto Minakawa, Kiyoshi Izumi, Hiroki Sakaji
TL;DR
This work reframes bilateral trade flow prediction as an edge-weight prediction problem within graph neural networks by introducing the Gravity-informed Graph Auto-encoder (GGAE) and a learnable surrogate decoder. By tying the gravity model $TradeFlow_{u,v} \approx \gamma \frac{GDP_u\,GDP_v}{distance(u,v)}$ to a GNN framework, the authors show that trade amounts can be recovered as edge weights using gravity-informed interactions $\mathbf{H}^e_{u,v} = \mathbf{H}_u \mathbf{H}_v^{T} \mathbf{E}_{u,v}^{-1}$, with decoders either linear ($\mathbf{A}^{amt}_{u,v} \approx \mathbf{W} \mathbf{H}^e_{u,v} + \mathbf{B}$) or via an $\text{MLP}$ surrogate. Experiments on the CEPII Gravity Database demonstrate that GGAE variants, especially with 2-layer GCNs, outperform the traditional gravity model in predicting trade amounts, and the surrogate decoder can offer robustness when gravity relationships are not perfectly satisfied. The approach highlights how incorporating topology and gravity-inspired decoding improves predictive power for complex, multi-country trade networks, and suggests broad applicability to other gravity-aligned systems such as migration or traffic networks.
Abstract
The gravity models has been studied to analyze interaction between two objects such as trade amount between a pair of countries, human migration between a pair of countries and traffic flow between two cities. Particularly in the international trade, predicting trade amount is instrumental to industry and government in business decision making and determining economic policies. Whereas the gravity models well captures such interaction between objects, the model simplifies the interaction to extract essential relationships or needs handcrafted features to drive the models. Recent studies indicate the connection between graph neural networks (GNNs) and the gravity models in international trade. However, to our best knowledge, hardly any previous studies in the this domain directly predicts trade amount by GNNs. We propose GGAE (Gravity-informed Graph Auto-encoder) and its surrogate model, which is inspired by the gravity model, showing trade amount prediction by the gravity model can be formulated as an edge weight prediction problem in GNNs and solved by GGAE and its surrogate model. Furthermore, we conducted experiments to indicate GGAE with GNNs can improve trade amount prediction compared to the traditional gravity model by considering complex relationships.