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  • Open Access

Human population dynamics as a Bayesian inverse transport problem

Chong Qi*

  • *Contact author: chongq@kth.se
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Phys. Rev. E 114, 054301 – Published 2 November, 2026

DOI: https://doi.org/10.1103/nrg2-2xj9

Abstract

Many open problems across physical, biological, and engineered systems involve nonequilibrium transport processes where the governing conservation laws are known, but the underlying constitutive relations remain latent and time varying. Conventional data-driven approaches like deep neural networks capture statistical patterns but routinely violate fundamental mass conservation. Here I introduce a unified Bayesian inverse transport framework that resolves this by embedding Bayesian neural networks directly within exact partial differential equations in age-time space. By evaluating this framework on complex, real-world human cohort advection across China, Japan, and South Korea, I demonstrate that this physical constraint enables consistent uncertainty propagation and missing-data reconstruction from sparse observations. Beyond demography, this framework provides a generalizable foundation for observing and forecasting nonequilibrium boundary dynamics across various fields.

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Phys. Rev. E 114, 054301– Published 2 November, 2026
  • Received 14 July 2026
  • Revised 28 September 2026
  • Accepted 20 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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