Neural optimization of the most probable paths of 3D active Brownian particles
Abstract
We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup variational principle for active systems and construct the Rayleighian of the ABP by including its active power. This approach reveals geometric transitions of the MPP from in-plane I- and U-shaped paths to 3D helical paths as the final time and net displacement are varied. We also demonstrate that the initial and final boundary conditions have a significant impact on the MPPs. Our results show that neural optimization combined with the Onsager-Machlup variational principle provides an efficient and versatile framework for exploring optimal transition pathways in active and nonequilibrium systems.
Keywords
Cite
@article{arxiv.2511.16178,
title = {Neural optimization of the most probable paths of 3D active Brownian particles},
author = {Bin Zheng and Zhongqiang Xiong and Changhao Li and Zhanglin Hou and Ziluo Zhang and Xinpeng Xu and Li-Shing Lin and Kenta Ishimoto and Kento Yasuda and Shigeyuki Komura},
journal= {arXiv preprint arXiv:2511.16178},
year = {2025}
}
Comments
6 pages, 3 figures