# On Exploring PDE Modeling for Point Cloud Video Representation Learning

arXiv: https://arxiv.org/abs/2404.04720 · HTML: https://mlsanity.com/paper/2404.04720/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 6 Apr 2024.

## Builds on (most cited first, 5 of 5)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [3DInAction: Understanding Human Actions in 3D Point Clouds](https://mlsanity.com/paper/2303.06346/) (2023)
- [Real-time 3D human action recognition based on Hyperpoint sequence](https://mlsanity.com/paper/2111.08492/) (2021)

## Built on by (most cited first, 2 of 2)

- [Content-Distortion High-Order Interaction for Blind Image Quality Assessment](https://mlsanity.com/paper/2504.05076/) (2025)
- [CL4D: Contrastive Language-4D Pretraining for Vision-Language Reasoning in Dynamic Scenes](https://mlsanity.com/paper/2608.18734/) (2026)

## Abstract (arXiv)

Point cloud video representation learning is challenging due to complex structures and unordered spatial arrangement. Traditional methods struggle with frame-to-frame correlations and point-wise correspondence tracking. Recently, partial differential equations (PDE) have provided a new perspective in uniformly solving spatial-temporal data information within certain constraints. While tracking tangible point correspondence remains challenging, we propose to formalize point cloud video representation learning as a PDE-solving problem. Inspired by fluid analysis, where PDEs are used to solve the deformation of spatial shape over time, we employ PDE to solve the variations of spatial points affected by temporal information. By modeling spatial-temporal correlations, we aim to regularize spatial variations with temporal features, thereby enhancing representation learning in point cloud videos. We introduce Motion PointNet composed of a PointNet-like encoder and a PDE-solving module. Initially, we construct a lightweight yet effective encoder to model an initial state of the spatial variations. Subsequently, we develop our PDE-solving module in a parameterized latent space, tailored to address the spatio-temporal correlations inherent in point cloud video. The process of solving PDE is guided and refined by a contrastive learning structure, which is pivotal in reshaping the feature distribution, thereby optimizing the feature representation within point cloud video data. Remarkably, our Motion PointNet achieves an impressive accuracy of 97.52% on the MSRAction-3D dataset, surpassing the current state-of-the-art in all aspects while consuming minimal resources (only 0.72M parameters and 0.82G FLOPs).