AI 中文总结
研究人口动态等非平衡输运问题，引入统一贝叶斯逆输运框架，将贝叶斯神经网络嵌入偏微分方程，通过对中日韩人类队列平流评估，实现不确定性传播和缺失数据重建，为跨领域非平衡边界动态观测预测提供基础。
AI 中文摘要
许多物理、生物和工程系统中的开放问题涉及非平衡输运过程，守恒定律已知，但本构关系未知且时变。传统数据驱动方法如深度神经网络虽能捕捉统计模式，但常违反质量守恒。本文引入统一的贝叶斯逆输运框架，将贝叶斯神经网络直接嵌入年龄-时间空间的精确偏微分方程来解决此问题。通过对中国、日本和韩国复杂的真实人类队列平流进行评估，证明该物理约束能实现一致的不确定性传播和从稀疏观测中重建缺失数据。该框架为跨领域观测和预测非平衡边界动态提供了可推广的基础。
英文摘要
Many open problems across physical, biological, and engineered systems involve non-equilibrium 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, we introduce a unified Bayesian inverse transport framework that resolves this by embedding Bayesian Neural Networks (BNNs) 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, we 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 non-equilibrium boundary dynamics across various fields.
Comments14 pages, 9 figures, 3 tables
