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 l...

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Published in:	Scientific reports Vol. 15; no. 1; pp. 18839 - 10
Main Authors:	Lee, Daekyung, Cho, Wonguk, Kim, Heetae, Kim, Gunn, Jeong, Hyeong-Chai, Kim, Beom Jun
Format:	Journal Article
Language:	English
Published:	London Nature Publishing Group UK 29.05.2025 Nature Publishing Group Nature Portfolio
Subjects:	639/766/259 639/766/530 Data-driven analysis Economics GDP Gravity model Gross Domestic Product Humanities and Social Sciences Inference algorithm International trade multidisciplinary Science Science (multidisciplinary) Trade flow Traffic control Gravity model Data-driven analysis Trade flow Inference algorithm
ISSN:	2045-2322, 2045-2322
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Abstract	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.
AbstractList	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.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. Abstract 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. 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.
ArticleNumber	18839
Author	Cho, Wonguk Kim, Gunn Kim, Heetae Lee, Daekyung Kim, Beom Jun Jeong, Hyeong-Chai
Author_xml	– sequence: 1 givenname: Daekyung surname: Lee fullname: Lee, Daekyung organization: Department of Energy Engineering, Korea Institute of Energy Technology, Supply Chain Intelligence Institute Austria – sequence: 2 givenname: Wonguk surname: Cho fullname: Cho, Wonguk organization: Graduate School of Data Science, Seoul National University – sequence: 3 givenname: Heetae surname: Kim fullname: Kim, Heetae organization: Department of Energy Engineering, Korea Institute of Energy Technology – sequence: 4 givenname: Gunn surname: Kim fullname: Kim, Gunn email: gunnkim@sejong.ac.kr organization: Department of Physics and Astronomy and Institute for Fundamental Physics, Sejong University – sequence: 5 givenname: Hyeong-Chai surname: Jeong fullname: Jeong, Hyeong-Chai organization: Department of Physics and Astronomy and Institute for Fundamental Physics, Sejong University, School of Computational Sciences, Korea Institute for Advanced Study – sequence: 6 givenname: Beom Jun surname: Kim fullname: Kim, Beom Jun email: beomjun@skku.edu organization: Department of Physics, Sungkyunkwan University
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Snippet	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,... 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,... Abstract 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...
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SubjectTerms	639/766/259 639/766/530 Data-driven analysis Economics GDP Gravity model Gross Domestic Product Humanities and Social Sciences Inference algorithm International trade multidisciplinary Science Science (multidisciplinary) Trade flow Traffic control
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Title	Self-consistent gravity model for inferring node mass in flow networks
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