Self-consistent gravity model for inferring node mass in flow networks

The gravity model, inspired by Newton's law of universal gravitation, has been a cornerstone in the analysis of trade flows between countries. In this model, each country is assigned an economic mass, where greater economic masses lead to stronger trade interactions. Traditionally, proxy variables like gross domestic product or other economic indicators have been used to approximate this economic mass. While these proxies offer convenient estimates of a country's economic size, they lack a direct theoretical connection to the actual drivers of trade flows, potentially leading to inconsistencies and misinterpretations. To address these limitations, we present a data-driven, self-consistent numerical approach that infers economic mass directly from trade flow data, eliminating the need for arbitrary proxies. Our approach, tested on synthetic data, accurately reconstructs predefined embeddings and system attributes, demonstrating robust predictive accuracy and flexibility. When applied to real-world trade networks, our method not only captures trade flows with precision but also distinguishes a country's intrinsic trade capacity from external factors, providing clearer insights into the key elements shaping the global trade landscape. This study marks a significant shift in the application of the gravity model, offering a more comprehensive tool for analyzing complex systems and revealing new insights across various fields, including global trade, traffic engineering, epidemic prevention, and infrastructure design.