# Fluid Dynamics Network: Topology-Agnostic 4D Reconstruction via Fluid Dynamics Priors

arXiv: https://arxiv.org/abs/2303.09871 · HTML: https://mlsanity.com/paper/2303.09871/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 59 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 30 of 31)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Neural-GIF: Neural Generalized Implicit Functions for Animating People in Clothing](https://mlsanity.com/paper/2108.08807/) (2021)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data](https://mlsanity.com/paper/2206.06577/) (2022)
- [Learning Parallel Dense Correspondence from Spatio-Temporal Descriptors for Efficient and Robust 4D Reconstruction](https://mlsanity.com/paper/2103.16341/) (2021)
- [A Multi-Pass GAN for Fluid Flow Super-Resolution](https://mlsanity.com/paper/1906.01689/) (2019)
- [Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids](https://mlsanity.com/paper/2009.06944/) (2020)
- [Dynamic Upsampling of Smoke through Dictionary-based Learning](https://mlsanity.com/paper/1910.09166/) (2019)
- [KiloNeuS: A Versatile Neural Implicit Surface Representation for Real-Time Rendering](https://mlsanity.com/paper/2206.10885/) (2022)

## Built on by (most cited first, 7 of 7)

- [NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos](https://mlsanity.com/paper/2312.06398/) (2023)
- [FreeGave: 3D Physics Learning from Dynamic Videos by Gaussian Velocity](https://mlsanity.com/paper/2506.07865/) (2025)
- [TRACE: Learning 3D Gaussian Physical Dynamics from Multi-view Videos](https://mlsanity.com/paper/2508.09811/) (2025)
- [DynoSurf: Neural Deformation-based Temporally Consistent Dynamic Surface Reconstruction](https://mlsanity.com/paper/2403.11586/) (2024)
- [Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis](https://mlsanity.com/paper/2503.03132/) (2025)
- [Regularizing Dynamic Radiance Fields with Kinematic Fields](https://mlsanity.com/paper/2407.14059/) (2024)
- [Accelerated Spatio-Temporal Gaussian Rendering via Kinematic and Semantic Priors](https://mlsanity.com/paper/2605.25909/) (2026)

## Abstract (arXiv)

Representing 3D surfaces as level sets of continuous functions over ℝ3 is the common denominator of neural implicit representations, which recently enabled remarkable progress in geometric deep learning and computer vision tasks. In order to represent 3D motion within this framework, it is often assumed (either explicitly or implicitly) that the transformations which a surface may undergo are homeomorphic: this is not necessarily true, for instance, in the case of fluid dynamics. In order to represent more general classes of deformations, we propose to apply this theoretical framework as regularizers for the optimization of simple 4D implicit functions (such as signed distance fields). We show that our representation is capable of capturing both homeomorphic and topology-changing deformations, while also defining correspondences over the continuously-reconstructed surfaces.