# Dual-frame Fluid Motion Estimation with Test-time Optimization and Zero-divergence Loss

arXiv: https://arxiv.org/abs/2410.11934 · HTML: https://mlsanity.com/paper/2410.11934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 101 references that are in the map.
- First posted on arXiv 15 Oct 2024.

## Builds on (most cited first, 30 of 53)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [Do We Really Need to Access the Source Data? Source Hypothesis Transfer for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2002.08546/) (2020)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [TAPIR: Tracking Any Point with per-frame Initialization and temporal Refinement](https://mlsanity.com/paper/2306.08637/) (2023)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Test-Time Training with Masked Autoencoders](https://mlsanity.com/paper/2209.07522/) (2022)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Depth Prediction Without the Sensors: Leveraging Structure for Unsupervised Learning from Monocular Videos](https://mlsanity.com/paper/1811.06152/) (2018)
- [DF-Net: Unsupervised Joint Learning of Depth and Flow using Cross-Task Consistency](https://mlsanity.com/paper/1809.01649/) (2018)
- [Self-supervised Learning with Geometric Constraints in Monocular Video: Connecting Flow, Depth, and Camera](https://mlsanity.com/paper/1907.05820/) (2019)
- [FLOT: Scene Flow on Point Clouds Guided by Optimal Transport](https://mlsanity.com/paper/2007.11142/) (2020)
- [RAFT-3D: Scene Flow using Rigid-Motion Embeddings](https://mlsanity.com/paper/2012.00726/) (2020)
- [f-BRS: Rethinking Backpropagating Refinement for Interactive Segmentation](https://mlsanity.com/paper/2001.10331/) (2020)
- [HPLFlowNet: Hierarchical Permutohedral Lattice FlowNet for Scene Flow Estimation on Large-scale Point Clouds](https://mlsanity.com/paper/1906.05332/) (2019)
- [Just Go with the Flow: Self-Supervised Scene Flow Estimation](https://mlsanity.com/paper/1912.00497/) (2019)
- [Self-supervised Learning of Motion Capture](https://mlsanity.com/paper/1712.01337/) (2017)
- [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021)
- [Test-Time Training on Nearest Neighbors for Large Language Models](https://mlsanity.com/paper/2305.18466/) (2023)
- [PV-RAFT: Point-Voxel Correlation Fields for Scene Flow Estimation of Point Clouds](https://mlsanity.com/paper/2012.00987/) (2020)
- [FlowStep3D: Model Unrolling for Self-Supervised Scene Flow Estimation](https://mlsanity.com/paper/2011.10147/) (2020)
- [Tent: Fully Test-time Adaptation by Entropy Minimization](https://mlsanity.com/paper/2006.10726/) (2020)
- [Self-Supervised Monocular Scene Flow Estimation](https://mlsanity.com/paper/2004.04143/) (2020)
- [Meta-DMoE: Adapting to Domain Shift by Meta-Distillation from Mixture-of-Experts](https://mlsanity.com/paper/2210.03885/) (2022)

## Built on by (most cited first, 1 of 1)

- [DeltaFlow: An Efficient Multi-frame Scene Flow Estimation Method](https://mlsanity.com/paper/2508.17054/) (2025)

## Abstract (arXiv)

3D particle tracking velocimetry (PTV) is a key technique for analyzing turbulent flow, one of the most challenging computational problems of our century. At the core of 3D PTV is the dual-frame fluid motion estimation algorithm, which tracks particles across two consecutive frames. Recently, deep learning-based methods have achieved impressive accuracy in dual-frame fluid motion estimation; however, they heavily depend on large volumes of labeled data. In this paper, we introduce a new method that is completely self-supervised and notably outperforms its fully-supervised counterparts while requiring only 1% of the training samples (without labels) used by previous methods. Our method features a novel zero-divergence loss that is specific to the domain of turbulent flow. Inspired by the success of splat operation in high-dimensional filtering and random fields, we propose a splat-based implementation for this loss which is both efficient and effective. The self-supervised nature of our method naturally supports test-time optimization, leading to the development of a tailored Dynamic Velocimetry Enhancer (DVE) module. We demonstrate that strong cross-domain robustness is achieved through test-time optimization on unseen leave-one-out synthetic domains and real physical/biological domains. Code, data and models are available at https://github.com/Forrest-110/FluidMotionNet.