发表机构
Laboratory for Disordered Systems, Phystech School of Applied Mathematics and Computer Science, Moscow Institute of Physics and Technology; Center for Computational Physics, Landau School for Physics and Research, Moscow Institute of Physics and Technology（莫斯科物理技术学院应用数学与计算机科学普列特赫学院无序系统实验室; 莫斯科物理技术学院朗道物理与研究中心计算物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对非晶介质中分子扩散的局域捕获态提取难题，提出基于离散莫尔斯拓扑骨架的结构信息贝叶斯正则化方法，消除传统几何算法偏差，在干酪根中成功解码受限扩散机制。
AI 中文摘要
分子在波动的非晶和高分子介质中的扩散主导着软物质物理、能量存储和生物膜中的关键输运过程。从单粒子追踪轨迹中提取局域捕获态仍然是一个基本挑战；由于热结构呼吸不断重构孔隙边界，传统几何算法遭受严重的系统性偏差，在分子循环返回过程中错误地合并不同的局域态。在此，我们通过将范式从局部几何递归转变为结构信息贝叶斯正则化来解决这一僵局。利用离散莫尔斯理论，我们提取波动宿主矩阵的时间不变拓扑骨架，以构建考虑单个分子尺寸的鲁棒、气体特异性物理先验。轨迹步骤通过两阶段概率细化顺序划分，动态适应输运景观。针对一个严格的环境进行基准测试，其中合成粒子探索实际互连的矩阵图，我们的方法消除了系统性偏差，在最优线性$O(N)$计算扩展下，将宏观捕获参数偏差限制在仅几个百分点内。应用于I型干酪根基质内的氢和甲烷输运，作为高度曲折、柔性高分子网络的原型，该方法成功解码了受限扩散的隐藏微观机制。为确保即时广泛影响，文档化的开源代码和数据已公开提供，提供了一种易于适应广泛追踪现象的可访问策略，从电池聚合物中的离子输运到细胞环境中的蛋白质运输。
英文摘要
Molecular diffusion in fluctuating amorphous and macromolecular media governs key transport processes across soft-matter physics, energy storage, and biological membranes. Extracting localized trapping states from single-particle tracking trajectories remains a fundamental challenge; because thermal structural breathing continuously reconfigures pore boundaries, conventional geometric algorithms suffer from severe systematic biases, erroneously merging distinct localized states during cyclic molecular returns. Here, we address this deadlock by shifting the paradigm from local geometric recurrence to a structure-informed Bayesian regularization. Leveraging discrete Morse theory, we extract the time-invariant topological skeleton of the fluctuating host matrix to construct robust, gas-specific physical priors that account for individual molecular dimensions. Trajectory steps are sequentially partitioned via a two-stage probabilistic refinement that dynamically adapts to the transport landscape. Benchmarked against a rigorous environment where synthetic particles explore the actual interconnected matrix graph, our approach eliminates systemic biases, restricting macroscopic trapping parameter deviations to just a few percent under optimal linear $O(N)$ computational scaling. Applied to hydrogen and methane transport within a type-I kerogen matrix, serving as a prototype for highly tortuous, flexible macromolecular networks, the method successfully decodes the hidden microscopic mechanisms of confined diffusion. To ensure immediate broad impact, the documented open-source code and data are made publicly available, offering an accessible strategy readily adaptable to a broad spectrum of tracking phenomena, from ion transport in battery polymers to protein trafficking within cellular environments.
Comments26 pages, 13 figures, 4 tables. Open-source code and reproducibility data are publicly available on GitHub and Zenodo
