Lagrangian Particle Optimization

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

CVPR 2024

Paper Video


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) [1] 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 [2], the physics is described by a material point method (MPM) [3], 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.


Example results

Example 1

Example 2

Example 3

Example 4


  title={Improving Physics-Augmented Continuum Neural Radiance Field-Based Geometry-Agnostic System Identification with Lagrangian Particle Optimization},
  author={Kaneko, Takuhiro},


  1. Xuan Li, Yi-Ling Qiao, Peter Yichen Chen, Krishna Murthy Jatavallabhula, Ming Lin, Chenfanfu Jiang, and Chuang Gan. PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification. In ICLR, 2023.
  2. Cheng Sun, Min Sun, and Hwann-Tzong Chen. Direct voxel grid optimization: Super-fast convergence for radiance fields reconstruction. In CVPR, 2022.
  3. Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand. DiffTaichi: Differentiable programming for physical simulation. In ICLR, 2020.