# Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization

arXiv: https://arxiv.org/abs/2406.04155 · HTML: https://mlsanity.com/paper/2406.04155/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 79 of its 92 references that are in the map.
- First posted on arXiv 6 Jun 2024.

## Builds on (most cited first, 30 of 79)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [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)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (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)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo](https://mlsanity.com/paper/2103.15595/) (2021)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)

## Built on by (most cited first, 16 of 16)

- [Generative Physical AI in Vision: A Survey](https://mlsanity.com/paper/2501.10928/) (2025)
- [Vid2Sim: Generalizable, Video-based Reconstruction of Appearance, Geometry and Physics for Mesh-free Simulation](https://mlsanity.com/paper/2506.06440/) (2025)
- [Grounding Creativity in Physics: A Brief Survey of Physical Priors in AIGC](https://mlsanity.com/paper/2502.07007/) (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)
- [Differentiable Physics-based System Identification for Robotic Manipulation of Elastoplastic Materials](https://mlsanity.com/paper/2411.00554/) (2024)
- [MOSIV: Multi-Object System Identification from Videos](https://mlsanity.com/paper/2603.06022/) (2026)
- [ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimation](https://mlsanity.com/paper/2506.05317/) (2025)
- [Gaussian-Augmented Physics Simulation and System Identification with Complex Colliders](https://mlsanity.com/paper/2511.06846/) (2025)
- [MonoPhysics: Estimating Geometry, Appearance, and Physical Parameters from Monocular Videos](https://mlsanity.com/paper/2605.30320/) (2026)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [HSImul3R: Physics-in-the-Loop Reconstruction of Simulation-Ready Human-Scene Interactions](https://mlsanity.com/paper/2603.15612/) (2026)
- [Structure from Collision](https://mlsanity.com/paper/2505.21335/) (2025)
- [MultiEcho: An Experimental Science of Learned Worlds](https://mlsanity.com/paper/2609.33347/) (2026)
- [VeloGauss: Learning Physically Consistent Gaussian Velocity Fields from Videos](https://mlsanity.com/paper/2605.10567/) (2026)
- [Learning Implicit Constitutive Laws for Dynamic 3D Gaussian Splatting from Monocular Videos](https://mlsanity.com/paper/2608.22102/) (2026)

## Abstract (arXiv)

Geometry-agnostic system identification is a technique for identifying the geometry and physical properties of an object from video sequences without any geometric assumptions. Recently, physics-augmented continuum neural radiance fields (PAC-NeRF) has demonstrated promising results for this technique by utilizing a hybrid Eulerian-Lagrangian representation, in which the geometry is represented by the Eulerian grid representations of NeRF, the physics is described by a material point method (MPM), and they are connected via Lagrangian particles. However, a notable limitation of PAC-NeRF is that its performance is sensitive to the learning of the geometry from the first frames owing to its two-step optimization. First, the grid representations are optimized with the first frames of video sequences, and then the physical properties are optimized through video sequences utilizing the fixed first-frame grid representations. This limitation can be critical when learning of the geometric structure is difficult, for example, in a few-shot (sparse view) setting. To overcome this limitation, we propose Lagrangian particle optimization (LPO), in which the positions and features of particles are optimized through video sequences in Lagrangian space. This method allows for the optimization of the geometric structure across the entire video sequence within the physical constraints imposed by the MPM. The experimental results demonstrate that the LPO is useful for geometric correction and physical identification in sparse-view settings.