Neural optimization of the most probable paths of 3D active Brownian particles

2025/11/20 by Zheng, Bin, Xiong, Zhongqiang, Li, Changhao +7
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Biological Physics (physics.bio-ph) #FOS: Physical sciences #Micro and Nano Robotics #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation

paper · doi:10.48550/arxiv.2511.16178

openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

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.

Citations

• Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics
• Demon's variational principle for informational active matter
• Emergence of odd elasticity in a microswimmer using deep reinforcement learning
• Deep learning-based computational method for soft matter dynamics: Deep Onsager-Machlup method
• Most probable paths for active Ornstein-Uhlenbeck particles
• Machine Learning for Phase Behavior in Active Matter Systems
• Stochastic thermodynamics, fluctuation theorems and molecular machines

Cited by

• Demon's variational principle for informational active matter

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