Structure-Informed Bayesian Inference of Anomalous Transport and Hidden Molecular Trapping in Amorphous Media
Abstract
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.
Related
- Explainable Molecular Structure Inference from GC--MS with Diffusion Models and LLM Reranking
- Structure-Transport Relationships in Aqueous Fructose Solutions: A Combined Molecular Dynamics and NMR Diffusion Study.
- Molecular dynamics between amorphous and crystalline phases of e-beam irradiated piezoelectric PVDF thin films employing solid-state NMR spectroscopy
- Machine Learning Prediction of Transport Properties in Amorphous Polymer Electrolytes Using Chemically Informed Structural Descriptors
- Automated loop invariant inference through learning-guided program structure analysis
BibTeX
@misc{ananev2026structureinformed,
title = {{Structure-Informed Bayesian Inference of Anomalous Transport and Hidden Molecular Trapping in Amorphous Media}},
author = {Andrey Ananev and Maria Potapova and Nikolay Kondratyuk and Timur Vostroknutov and Aleksey Khlyupin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08780},
eprint = {2609.08780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08780},
}
RIS
TY - UNPB
TI - Structure-Informed Bayesian Inference of Anomalous Transport and Hidden Molecular Trapping in Amorphous Media
AU - Andrey Ananev
AU - Maria Potapova
AU - Nikolay Kondratyuk
AU - Timur Vostroknutov
AU - Aleksey Khlyupin
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08780
UR - https://arxiv.org/abs/2609.08780
AB - 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.
ER -