Neural optimization of the most probable paths of 3D active Brownian particles
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arXiv
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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911277872316416 |
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| author | Zheng, Bin Xiong, Zhongqiang Li, Changhao Hou, Zhanglin Zhang, Ziluo Xu, Xinpeng Lin, Li-Shing Ishimoto, Kenta Yasuda, Kento Komura, Shigeyuki |
| author_facet | Zheng, Bin Xiong, Zhongqiang Li, Changhao Hou, Zhanglin Zhang, Ziluo Xu, Xinpeng Lin, Li-Shing Ishimoto, Kenta Yasuda, Kento Komura, Shigeyuki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16178 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neural optimization of the most probable paths of 3D active Brownian particles Zheng, Bin Xiong, Zhongqiang Li, Changhao Hou, Zhanglin Zhang, Ziluo Xu, Xinpeng Lin, Li-Shing Ishimoto, Kenta Yasuda, Kento Komura, Shigeyuki Soft Condensed Matter Statistical Mechanics Biological Physics 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. |
| title | Neural optimization of the most probable paths of 3D active Brownian particles |
| topic | Soft Condensed Matter Statistical Mechanics Biological Physics |
| url | https://arxiv.org/abs/2511.16178 |