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Dual-frame Fluid Motion Estimation with Test-time Optimization and Zero-divergence Loss
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Proposes a fully self-supervised dual-frame 3D fluid motion estimator with a splat-based zero-divergence loss and a test-time residual optimization module (DVE), matching or beating supervised methods with 1% of training samples and no labels.
Problem
Dual-frame 3D particle tracking velocimetry (PTV) fluid motion estimation relies on large fully labeled datasets, which are costly to collect, and supervised models generalize poorly across domains.
Approach
Train a graph-based optimal-transport flow estimator purely self-supervised using reconstruction, smoothness, and a zero-divergence loss computed by splatting unstructured particle flows onto a uniform grid; then refine the flow on each test input via a test-time residual optimization (DVE) using only the reconstruction loss.
Key results
- Self-supervised model trained on 1% of FluidFlow3D (130 samples) reaches EPE 0.00850 with 97.61% Acc Strict on the full training-size setting, versus GotFlow3D (all data, supervised) at 0.00487 EPE and 93.15% Acc Strict (10% and 1% GotFlow3D reach 0.02032 and 0.02773 EPE).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the proposed method instead of GotFlow3D | FluidFlow3D motion estimation · Forced MHD Turbulence | EPE: 0.00596 -> 0.0037 | Helped |
| use the proposed method instead of GotFlow3D | FluidFlow3D motion estimation · Forced Isotropic Turbulence | EPE: 0.01153 -> 0.0117 | Hurt |
| use the proposed method instead of GotFlow3D | FluidFlow3D motion estimation · Turbulent Channel Flow | EPE: 0.00241 -> 0.0019 | Helped |
| train the proposed method with 1% rather than all training data | Ours on FluidFlow3D · FluidFlow3D test data | EPE: 0.00460 -> 0.00850 | Hurt |
| use Ours+Fm initialization instead of Fm-track alone | Fm-track on AVIC · AVIC C2N | MNDS: 0.283 -> 0.246 | Helped |
| use Ours+Fm initialization instead of Fm-track alone | Fm-track on AVIC · AVIC E2N | tracked matches: 8097 -> 8097 | No clear effect |
| use Ours+Fm initialization instead of Fm-track alone | Fm-track on AVIC · AVIC C2E | tracked matches: 8040 -> 8048 | Helped |
Surprising findings
- Self-supervised training on only 1% of samples outperforms fully supervised GotFlow3D trained on all data in the per-case FluidFlow3D tables.
Limitations
- DeformationFlow evaluation is qualitative only because no ground truth is available, and AVIC improvements over Fm-track are slight.
- Zero-divergence loss assumes incompressible flow, which the paper notes does not hold for DeformationFlow.
- Real-world validation is limited to two datasets and integration with PTV pipelines.
Experimental setup
Datasets: FluidFlow3D DeformationFlow AVIC
Benchmarks: FluidFlow3D DeformationFlow AVIC
Metrics: EPE NEPE Acc Strict Acc Relax Outliers Matches Tracking ratio neighbor distance score
Baselines: FlowNet3D FLOT PointPWC-Net PV-RAFT GotFlow3D
Builds on: GotFlow3D FLOT Chamfer distance EdgeConv
Closest papers by meaning
- Spike Imaging Velocimetry: Dense Motion Estimation of Fluids Using Spike Streams (AAAI 2026 · similarity 0.89)
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- Minimizing $f$-Divergences by Interpolating Velocity Fields (ICML 2024 · similarity 0.83)
- DGS-LRM: Real-Time Deformable 3D Gaussian Reconstruction From Monocular Videos (NeurIPS 2025 · similarity 0.83)
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- Accelerating Rectified Flow Models via Trajectory-Aware Caching (NeurIPS 2026 · similarity 0.82)
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