# NVFi: Neural Velocity Fields for 3D Physics Learning from Dynamic Videos

arXiv: https://arxiv.org/abs/2312.06398 · HTML: https://mlsanity.com/paper/2312.06398/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 75 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 30 of 63)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [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)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Video](https://mlsanity.com/paper/2201.04127/) (2022)
- [Dynamic Neural Radiance Fields for Monocular 4D Facial Avatar Reconstruction](https://mlsanity.com/paper/2012.03065/) (2020)
- [One-Shot Free-View Neural Talking-Head Synthesis for Video Conferencing](https://mlsanity.com/paper/2011.15126/) (2020)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)

## Built on by (most cited first, 28 of 28)

- [GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation](https://mlsanity.com/paper/2406.14927/) (2024)
- [Generative Physical AI in Vision: A Survey](https://mlsanity.com/paper/2501.10928/) (2025)
- [FreeGave: 3D Physics Learning from Dynamic Videos by Gaussian Velocity](https://mlsanity.com/paper/2506.07865/) (2025)
- [ODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splatting](https://mlsanity.com/paper/2506.05480/) (2025)
- [TRACE: Learning 3D Gaussian Physical Dynamics from Multi-view Videos](https://mlsanity.com/paper/2508.09811/) (2025)
- [MASIV: Toward Material-Agnostic System Identification from Videos](https://mlsanity.com/paper/2508.01112/) (2025)
- [PhysInOne: Visual Physics Learning and Reasoning in One Suite](https://mlsanity.com/paper/2604.09415/) (2026)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [Seeing the Wind from a Falling Leaf](https://mlsanity.com/paper/2512.00762/) (2025)
- [MOSIV: Multi-Object System Identification from Videos](https://mlsanity.com/paper/2603.06022/) (2026)
- [Advances in Radiance Field for Dynamic Scene: From Neural Field to Gaussian Field](https://mlsanity.com/paper/2505.10049/) (2025)
- [ParticleGS: Learning Neural Gaussian Particle Dynamics from Videos for Prior-free Physical Motion Extrapolation](https://mlsanity.com/paper/2505.20270/) (2025)
- [ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimation](https://mlsanity.com/paper/2506.05317/) (2025)
- [Advances in 4D Representation: Geometry, Motion, and Interaction](https://mlsanity.com/paper/2510.19255/) (2025)
- [ExFMan: Rendering 3D Dynamic Humans with Hybrid Monocular Blurry Frames and Events](https://mlsanity.com/paper/2409.14103/) (2024)
- [Lie Flow: Video Dynamic Fields Modeling and Predicting with Lie Algebra as Geometric Physics Principle](https://mlsanity.com/paper/2602.21645/) (2026)
- [Reconstructing the Dynamic World: A Representation-Centric View of 4D Scene Reconstruction](https://mlsanity.com/paper/2609.39960/) (2026)
- [OSN: Infinite Representations of Dynamic 3D Scenes from Monocular Videos](https://mlsanity.com/paper/2407.05615/) (2024)
- [Hierarchically Structured Neural Bones for Reconstructing Animatable Objects from Casual Videos](https://mlsanity.com/paper/2408.00351/) (2024)
- [Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation](https://mlsanity.com/paper/2510.24216/) (2025)
- [GS-DMSR: Dynamic Sensitive Multi-scale Manifold Enhancement for Accelerated High-Quality 3D Gaussian Splatting](https://mlsanity.com/paper/2601.05584/) (2026)
- [VeloGauss: Learning Physically Consistent Gaussian Velocity Fields from Videos](https://mlsanity.com/paper/2605.10567/) (2026)
- [CausalGS: Learning Physical Causality of 3D Dynamic Scenes with Gaussian Representations](https://mlsanity.com/paper/2605.10586/) (2026)
- [Accelerated Spatio-Temporal Gaussian Rendering via Kinematic and Semantic Priors](https://mlsanity.com/paper/2605.25909/) (2026)
- [PhysMani: Physics-principled 3D World Model for Dynamic Object Manipulation](https://mlsanity.com/paper/2607.01938/) (2026)
- [GrowFields: Compositional 4D Neural Fields for Topology-Changing Plant Growth](https://mlsanity.com/paper/2607.03330/) (2026)
- [LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting](https://mlsanity.com/paper/2608.16324/) (2026)
- [LagrangeGS: Non-Conservative Lagrangian System on Dynamic 3D Gaussian Splatting](https://mlsanity.com/paper/2608.22773/) (2026)

## Abstract (arXiv)

In this paper, we aim to model 3D scene dynamics from multi-view videos. Unlike the majority of existing works which usually focus on the common task of novel view synthesis within the training time period, we propose to simultaneously learn the geometry, appearance, and physical velocity of 3D scenes only from video frames, such that multiple desirable applications can be supported, including future frame extrapolation, unsupervised 3D semantic scene decomposition, and dynamic motion transfer. Our method consists of three major components, 1) the keyframe dynamic radiance field, 2) the interframe velocity field, and 3) a joint keyframe and interframe optimization module which is the core of our framework to effectively train both networks. To validate our method, we further introduce two dynamic 3D datasets: 1) Dynamic Object dataset, and 2) Dynamic Indoor Scene dataset. We conduct extensive experiments on multiple datasets, demonstrating the superior performance of our method over all baselines, particularly in the critical tasks of future frame extrapolation and unsupervised 3D semantic scene decomposition.