# Global Transport for Fluid Reconstruction with Learned Self-Supervision

arXiv: https://arxiv.org/abs/2104.06031 · HTML: https://mlsanity.com/paper/2104.06031/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 82 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)
- [Learning Category-Specific Mesh Reconstruction from Image Collections](https://mlsanity.com/paper/1803.07549/) (2018)
- [State of the Art on Neural Rendering](https://mlsanity.com/paper/2004.03805/) (2020)
- [The relativistic discriminator: a key element missing from standard GAN](https://mlsanity.com/paper/1807.00734/) (2018)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [How Much Position Information Do Convolutional Neural Networks Encode?](https://mlsanity.com/paper/2001.08248/) (2020)
- [Escaping Plato's Cave: 3D Shape From Adversarial Rendering](https://mlsanity.com/paper/1811.11606/) (2018)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [V2V-PoseNet: Voxel-to-Voxel Prediction Network for Accurate 3D Hand and Human Pose Estimation from a Single Depth Map](https://mlsanity.com/paper/1711.07399/) (2017)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Sparse Surface Constraints for Combining Physics-based Elasticity Simulation and Correspondence-Free Object Reconstruction](https://mlsanity.com/paper/1910.01812/) (2019)
- [Lagrangian Neural Style Transfer for Fluids](https://mlsanity.com/paper/2005.00803/) (2020)
- [Transport-Based Neural Style Transfer for Smoke Simulations](https://mlsanity.com/paper/1905.07442/) (2019)
- [Coupled Fluid Density and Motion from Single Views](https://mlsanity.com/paper/1806.06613/) (2018)
- [Single-image Tomography: 3D Volumes from 2D Cranial X-Rays](https://mlsanity.com/paper/1710.04867/) (2017)

## Built on by (most cited first, 18 of 18)

- [Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data](https://mlsanity.com/paper/2206.06577/) (2022)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2312.05320/) (2023)
- [FluidNexus: 3D Fluid Reconstruction and Prediction from a Single Video](https://mlsanity.com/paper/2503.04720/) (2025)
- [Inferring Hybrid Neural Fluid Fields from Videos](https://mlsanity.com/paper/2312.06561/) (2023)
- [Fluid Simulation on Neural Flow Maps](https://mlsanity.com/paper/2312.14635/) (2023)
- [Physics-Informed Learning of Characteristic Trajectories for Smoke Reconstruction](https://mlsanity.com/paper/2407.09679/) (2024)
- [Learning to Estimate Single-View Volumetric Flow Motions without 3D Supervision](https://mlsanity.com/paper/2302.14470/) (2023)
- [Representing Flow Fields with Divergence-Free Kernels for Reconstruction](https://mlsanity.com/paper/2504.01913/) (2025)
- [Image Based Reconstruction of Liquids from 2D Surface Detections](https://mlsanity.com/paper/2111.11491/) (2021)
- [Data-Efficient Inference of Neural Fluid Fields via SciML Foundation Model](https://mlsanity.com/paper/2412.13897/) (2024)
- [Learning an Implicit Physics Model for Image-based Fluid Simulation](https://mlsanity.com/paper/2508.08254/) (2025)
- [Volumetric Cloud Field Reconstruction](https://mlsanity.com/paper/2311.17657/) (2023)
- [LagrangianSplats: Divergence-Free Transport of Gaussian Primitives for Fluid Reconstruction](https://mlsanity.com/paper/2605.09299/) (2026)
- [SurfPhase: 3D Interfacial Dynamics in Two-Phase Flows from Sparse Videos](https://mlsanity.com/paper/2602.11154/) (2026)
- [Light Transport-aware Diffusion Posterior Sampling for Single-View Reconstruction of 3D Volumes](https://mlsanity.com/paper/2501.05226/) (2025)
- [SmokeSVD: Smoke Reconstruction from A Single View via Progressive Novel View Synthesis and Refinement with Diffusion Models](https://mlsanity.com/paper/2507.12156/) (2025)
- [SplashSplat: Reconstructing Splashing Liquids from Real-World Multi-View Videos](https://mlsanity.com/paper/2609.20818/) (2026)

## Abstract (arXiv)

We propose a novel method to reconstruct volumetric flows from sparse views via a global transport formulation. Instead of obtaining the space-time function of the observations, we reconstruct its motion based on a single initial state. In addition we introduce a learned self-supervision that constrains observations from unseen angles. These visual constraints are coupled via the transport constraints and a differentiable rendering step to arrive at a robust end-to-end reconstruction algorithm. This makes the reconstruction of highly realistic flow motions possible, even from only a single input view. We show with a variety of synthetic and real flows that the proposed global reconstruction of the transport process yields an improved reconstruction of the fluid motion.