# Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data

arXiv: https://arxiv.org/abs/2206.06577 · HTML: https://mlsanity.com/paper/2206.06577/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 91 references that are in the map.
- First posted on arXiv 14 Jun 2022.

## Builds on (most cited first, 30 of 52)

- [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)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis](https://mlsanity.com/paper/2110.08985/) (2021)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [Dynamic Neural Radiance Fields for Monocular 4D Facial Avatar Reconstruction](https://mlsanity.com/paper/2012.03065/) (2020)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [DeepVoxels: Learning Persistent 3D Feature Embeddings](https://mlsanity.com/paper/1812.01024/) (2018)

## Built on by (most cited first, 30 of 52)

- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [3D Gaussian as a New Era: A Survey](https://mlsanity.com/paper/2402.07181/) (2024)
- [Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians](https://mlsanity.com/paper/2403.09434/) (2024)
- [PhysTwin: Physics-Informed Reconstruction and Simulation of Deformable Objects from Videos](https://mlsanity.com/paper/2503.17973/) (2025)
- [PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation](https://mlsanity.com/paper/2509.20358/) (2025)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos](https://mlsanity.com/paper/2312.06398/) (2023)
- [Recent Trends in 3D Reconstruction of General Non-Rigid Scenes](https://mlsanity.com/paper/2403.15064/) (2024)
- [Dynamic Mesh-Aware Radiance Fields](https://mlsanity.com/paper/2309.04581/) (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)
- [Learning Vortex Dynamics for Fluid Inference and Prediction](https://mlsanity.com/paper/2301.11494/) (2023)
- [Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization](https://mlsanity.com/paper/2406.04155/) (2024)
- [FreeGave: 3D Physics Learning from Dynamic Videos by Gaussian Velocity](https://mlsanity.com/paper/2506.07865/) (2025)
- [Fluid Simulation on Neural Flow Maps](https://mlsanity.com/paper/2312.14635/) (2023)
- [Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent Parametric Partial Differential Equations](https://mlsanity.com/paper/2406.03919/) (2024)
- [ElastoGen: 4D Generative Elastodynamics](https://mlsanity.com/paper/2405.15056/) (2024)
- [Physics-Informed Learning of Characteristic Trajectories for Smoke Reconstruction](https://mlsanity.com/paper/2407.09679/) (2024)
- [Fluid Dynamics Network: Topology-Agnostic 4D Reconstruction via Fluid Dynamics Priors](https://mlsanity.com/paper/2303.09871/) (2023)
- [SmokeSeer: 3D Gaussian Splatting for Smoke Removal and Scene Reconstruction](https://mlsanity.com/paper/2509.17329/) (2025)
- [Physics-Informed Deformable Gaussian Splatting: Towards Unified Constitutive Laws for Time-Evolving Material Field](https://mlsanity.com/paper/2511.06299/) (2025)
- [Learning to Estimate Single-View Volumetric Flow Motions without 3D Supervision](https://mlsanity.com/paper/2302.14470/) (2023)
- [FFEINR: Flow Feature-Enhanced Implicit Neural Representation for Spatio-temporal Super-Resolution](https://mlsanity.com/paper/2308.12508/) (2023)
- [Scaling Face Interaction Graph Networks to Real World Scenes](https://mlsanity.com/paper/2401.11985/) (2024)
- [Representing Flow Fields with Divergence-Free Kernels for Reconstruction](https://mlsanity.com/paper/2504.01913/) (2025)
- [ParticleGS: Learning Neural Gaussian Particle Dynamics from Videos for Prior-free Physical Motion Extrapolation](https://mlsanity.com/paper/2505.20270/) (2025)
- [Regularizing Dynamic Radiance Fields with Kinematic Fields](https://mlsanity.com/paper/2407.14059/) (2024)
- [Data-Efficient Inference of Neural Fluid Fields via SciML Foundation Model](https://mlsanity.com/paper/2412.13897/) (2024)
- [ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimation](https://mlsanity.com/paper/2506.05317/) (2025)

## Abstract (arXiv)

High-fidelity reconstruction of fluids from sparse multiview RGB videos remains a formidable challenge due to the complexity of the underlying physics as well as complex occlusion and lighting in captures. Existing solutions either assume knowledge of obstacles and lighting, or only focus on simple fluid scenes without obstacles or complex lighting, and thus are unsuitable for real-world scenes with unknown lighting or arbitrary obstacles. We present the first method to reconstruct dynamic fluid by leveraging the governing physics (ie, Navier -Stokes equations) in an end-to-end optimization from sparse videos without taking lighting conditions, geometry information, or boundary conditions as input. We provide a continuous spatio-temporal scene representation using neural networks as the ansatz of density and velocity solution functions for fluids as well as the radiance field for static objects. With a hybrid architecture that separates static and dynamic contents, fluid interactions with static obstacles are reconstructed for the first time without additional geometry input or human labeling. By augmenting time-varying neural radiance fields with physics-informed deep learning, our method benefits from the supervision of images and physical priors. To achieve robust optimization from sparse views, we introduced a layer-by-layer growing strategy to progressively increase the network capacity. Using progressively growing models with a new regularization term, we manage to disentangle density-color ambiguity in radiance fields without overfitting. A pretrained density-to-velocity fluid model is leveraged in addition as the data prior to avoid suboptimal velocity which underestimates vorticity but trivially fulfills physical equations. Our method exhibits high-quality results with relaxed constraints and strong flexibility on a representative set of synthetic and real flow captures.