mlsanityData to 7 Oct 2026

VPNets: Volume-preserving neural networks for learning source-free dynamics

arXiv 2204.13843 ↗First posted 29 Apr 2022cs.LGcited by 2

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Abstract (arXiv)

We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two network architectures, coined R-VPNet and LA-VPNet. The distinct feature of the proposed models is that they are intrinsic volume-preserving. In addition, the corresponding approximation theorems are proved, which theoretically guarantee the expressivity of the proposed VPNets to learn source-free dynamics. The effectiveness, generalization ability and structure-preserving property of the VP-Nets are demonstrated by numerical experiments.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 24 of its 46 references that are in the map. First posted on arXiv 29 Apr 2022.

Builds on

24 of 46 references.

References · 24

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12 more
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 1.

2 papers.

  1. 2024Learning Non-Linear Invariants for Unsupervised Out-of-Distribution Detectioncited by 0
  2. 2026LLN: Learnable Lens Networks for Parameter-Efficient Long-Horizon Dynamical Predictioncited by 0