Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918008993087488 |
|---|---|
| author | Xu, Ruichen Wu, Zongyu Chen, Luoyao Kementzidis, Georgios Wang, Siyao Wang, Haochun Shi, Yiwei Deng, Yuefan |
| author_facet | Xu, Ruichen Wu, Zongyu Chen, Luoyao Kementzidis, Georgios Wang, Siyao Wang, Haochun Shi, Yiwei Deng, Yuefan |
| contents | Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work, we introduce a method to train a standard Hamiltonian Neural Network (HNN) using only position data, enabled by a theoretical result that permits transforming the Hamiltonian $H(q,p)$ into a form $H(q, v)$. Under certain assumptions, namely, an invertible relationship between momentum and velocity, we formally prove the validity of this substitution and demonstrate how it allows us to infer momentum from position alone. We apply our approach to canonical examples including the spring-mass system, pendulum, two-body, and three-body problems. Our results show that using only position data is sufficient for stable and energy-consistent long-term predictions, suggesting a promising pathway for data-driven discovery of Hamiltonian systems when momentum measurements are unavailable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data Xu, Ruichen Wu, Zongyu Chen, Luoyao Kementzidis, Georgios Wang, Siyao Wang, Haochun Shi, Yiwei Deng, Yuefan Computational Physics 37M25, 68T07, 37J10, 70H05 I.2.6; I.2.8; G.1.7 Data-driven modeling of physical systems often relies on learning both positions and momenta to accurately capture Hamiltonian dynamics. However, in many practical scenarios, only position measurements are readily available. In this work, we introduce a method to train a standard Hamiltonian Neural Network (HNN) using only position data, enabled by a theoretical result that permits transforming the Hamiltonian $H(q,p)$ into a form $H(q, v)$. Under certain assumptions, namely, an invertible relationship between momentum and velocity, we formally prove the validity of this substitution and demonstrate how it allows us to infer momentum from position alone. We apply our approach to canonical examples including the spring-mass system, pendulum, two-body, and three-body problems. Our results show that using only position data is sufficient for stable and energy-consistent long-term predictions, suggesting a promising pathway for data-driven discovery of Hamiltonian systems when momentum measurements are unavailable. |
| title | Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data |
| topic | Computational Physics 37M25, 68T07, 37J10, 70H05 I.2.6; I.2.8; G.1.7 |
| url | https://arxiv.org/abs/2505.02321 |