Neural network modeling of longitudinal oscillations of a rope with a moving boundary

Title	Neural network modeling of longitudinal oscillations of a rope with a moving boundary
Authors	V. L. Litvinov¹, K. V. Litvinova² ¹Samara State Technical University ²Lomonosov Moscow State University
Annotation	An approach to calculating free longitudinal oscillations of a variable-length rope is proposed, based on the use of physically-informed neural networks. Unlike classical analytical methods, the network is trained directly in the domain with a moving boundary, without transitioning to fixed coordinates. The resulting solution is in good agreement with existing results. The method can be extended to more complex laws of boundary motion, taking into account dissipative factors.
Keywords	wave equation, variable-length rope, moving boundary, machine learning, physically-informed neural networkss.
Citation	Litvinov V. L., Litvinova K. V. ''Neural network modeling of longitudinal oscillations of a rope with a moving boundary'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 126-129. Available at: https://conf.svmo.ru/files/2026/papers/paper88.pdf. - Date of access: 25.09.2026.