中国物理B ›› 2025, Vol. 34 ›› Issue (5): 50205-050205.doi: 10.1088/1674-1056/adcb99

所属专题: SPECIAL TOPIC — Computational programs in complex systems

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Trajectory tracking on the optimal path of two-dimensional quadratic barrier escaping

Zengxuan Zhao(赵曾轩)1, Xiuying Zhang(张秀颖)1, Pengchen Zhao(赵鹏琛)1, Chunyang Wang(王春阳)1,2,†, Chunlei Xia(夏春雷)2, Mushtaq Rana Imran1, and Joelous Malamula Nyasulu1   

  1. 1 Institute of Theoretical Physics, School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China;
    2 Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China
  • 收稿日期:2024-12-24 修回日期:2025-04-09 接受日期:2025-04-11 出版日期:2025-05-15 发布日期:2025-05-06
  • 通讯作者: Chunyang Wang E-mail:wchy@foxmail.com
  • 基金资助:
    This work was supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2020MA092) and the Innovation Project for Graduate Students of Ludong University (Grant No. IPGS2024-048).

Trajectory tracking on the optimal path of two-dimensional quadratic barrier escaping

Zengxuan Zhao(赵曾轩)1, Xiuying Zhang(张秀颖)1, Pengchen Zhao(赵鹏琛)1, Chunyang Wang(王春阳)1,2,†, Chunlei Xia(夏春雷)2, Mushtaq Rana Imran1, and Joelous Malamula Nyasulu1   

  1. 1 Institute of Theoretical Physics, School of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China;
    2 Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China
  • Received:2024-12-24 Revised:2025-04-09 Accepted:2025-04-11 Online:2025-05-15 Published:2025-05-06
  • Contact: Chunyang Wang E-mail:wchy@foxmail.com
  • Supported by:
    This work was supported by the Natural Science Foundation of Shandong Province (Grant No. ZR2020MA092) and the Innovation Project for Graduate Students of Ludong University (Grant No. IPGS2024-048).

摘要: The diffusion trajectory of a Brownian particle passing over the saddle point of a two-dimensional quadratic potential energy surface is tracked in detail according to the deep learning strategies. Generative adversarial networks (GANs) emanating in the category of machine learning (ML) frameworks are used to generate and assess the rationality of the data. While their optimization is based on the long short-term memory (LSTM) strategies. In addition to drawing a heat map, the optimal path of two-dimensional (2D) diffusion is simultaneously demonstrated in a stereoscopic space. The results of our simulation are completely consistent with the previous theoretical predictions.

关键词: trajectory tracking, optimal path, two-dimensional barrier escaping, deep learning

Abstract: The diffusion trajectory of a Brownian particle passing over the saddle point of a two-dimensional quadratic potential energy surface is tracked in detail according to the deep learning strategies. Generative adversarial networks (GANs) emanating in the category of machine learning (ML) frameworks are used to generate and assess the rationality of the data. While their optimization is based on the long short-term memory (LSTM) strategies. In addition to drawing a heat map, the optimal path of two-dimensional (2D) diffusion is simultaneously demonstrated in a stereoscopic space. The results of our simulation are completely consistent with the previous theoretical predictions.

Key words: trajectory tracking, optimal path, two-dimensional barrier escaping, deep learning

中图分类号:  (Computational techniques; simulations)

  • 02.70.-c
05.40.Jc (Brownian motion) 07.05.Bx (Computer systems: hardware, operating systems, computer languages, and utilities)