SPS-GAN：从学习到的哈密顿系统中发现相空间结构
Discovering Phase Space Structure in Learned Hamiltonian Systems
AI 导读
研究者提出结构化相空间生成对抗网络 SPS-GAN，一个条件生成框架，可从笛卡尔轨迹或视频观测中学习力学动力学并发现潜在相空间结构。该方法将对抗生成与 port-Hamiltonian 潜在动力学结合，并扩展循环坐标正则化以处理耗散与外力，支持保守、耗散和受迫系统。模拟与真实系统实验显示其轨迹精度和视频生成质量优于竞争基线，并能识别出与有效自由度一致的活跃潜在维度。
正文 · 原文
Abstract:Mechanics-inspired neural networks provide physically structured models of dynamical systems, but typically assume access to the coordinates in which the underlying dynamics are expressed. While recent generative approaches relax this assumption, they remain limited in their ability to jointly model different dynamical regimes and discover interpretable latent structure. We introduce Structured Phase Space GAN (SPS-GAN), a conditional generative framework that learns mechanical dynamics and discovers latent phase-space structure from Cartesian trajectories or video observations. We achieve this by combining adversarial generation with port-Hamiltonian latent dynamics and extending cyclic-coordinate regularization to account for dissipation and forcing. This formulation supports conservative, dissipative, and forced systems while encouraging compact latent representations from which active degrees of freedom can be identified. Experiments on simulated and real-world systems demonstrate improved trajectory accuracy and video generation quality over competitive baselines, while identifying active latent dimensions consistent with the expected effective degrees of freedom and recovering physically interpretable coordinates across observation modalities and dynamical regimes.
| Comments: | Accept to the 40th Annual Conference on Neural Information Processing Systems (NeurIPS 2026) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Systems and Control (eess.SY) |
| Cite as: | arXiv:2509.23003 [cs.LG] |
| (or arXiv:2509.23003v4 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2509.23003 arXiv-issued DOI via DataCite |
Submission history
From: Yulong Yang [view email]
[v1]
Fri, 26 Sep 2025 23:46:55 UTC (7,705 KB)
[v2]
Wed, 14 Jan 2026 17:15:25 UTC (8,482 KB)
[v3]
Thu, 8 Oct 2026 20:45:56 UTC (12,455 KB)
[v4]
Wed, 4 Nov 2026 03:21:18 UTC (12,579 KB)
来源：arXiv cs.AI · arxiv.org