ElastoGen: 4D Generative Elastodynamics

Yutao Feng1,2*, Yintong Shang1*, Xiang Feng1,2*, Lei Lan1, Shandian Zhe1, Tianjia Shao2, Hongzhi Wu2, Kun Zhou2, Hao Su3, Chenfanfu Jiang4, Yin Yang1
University of Utah1, Zhejiang University2, University of California, San Diego3, University of California, Los Angeles4
*: contribute equally.
Paper arXiv Video Code(coming soon)
Utah ZJU UCSD UCLA

ElastoGen is a knowledge-driven model that generates physically accurate and coherent 4D elastodynamics.

Abstract

We present ElastoGen, a knowledge-driven model that generates physically accurate and coherent 4D elastodynamics. Instead of relying on petabyte-scale data-driven learning, ElastoGen leverages the principles of physics-in-the-loop and learns from established physical knowledge, such as partial differential equations and their numerical solutions. The core idea of ElastoGen is converting the global differential operator, corresponding to the nonlinear elastodynamic equations, into iterative local convolution-like operations, which naturally fit modern neural networks. Each network module is specifically designed to support this goal rather than functioning as a black box. As a result, ElastoGen is exceptionally lightweight in terms of both training requirements and network scale. Additionally, due to its alignment with physical procedures, ElastoGen efficiently generates accurate dynamics for a wide range of hyperelastic materials and can be easily integrated with upstream and downstream deep modules to enable end-to-end 4D generation.

Pipeline & Network Architecture



ElastoGen inputs a voxelized 3D model and boundary conditions, using physical parameters to generate ElaNet's weights via a diffusion model. ElaNet performs local and global optimizations to compute elastic dynamics.


Adhering to physical laws, our architecture achieves accurate dynamics for hyperelastic materials with minimal parameterization. The network updates positions using ElaNet for local projections and global solving.

Experiments


Feasibility across Various Shapes: To demonstrate the feasibility of our method across various shapes, we conduct experiments on multiple models from ShapeNet with different force and pin settings. Click on image to zoom in.

Versatility across Geometric Representations: Our method can be applied to any geometric representation. For instance, when using implicit Neural Radiance Fields (NeRF) to describe 3D models, we employ the technique from PIE-NeRF. We first voxelize the NeRF based on the density fields. Then, we generate dynamics using ElastoGen and finally obtain a dynamic NeRF through linear ray warping.

Capability on Complex Meshes: Our method is also applicable to complex explicit meshes. We test our approach on meshes with intricate geometries, achieving similarly impressive results. With adaptive resolution for voxelization, ElastoGen produces visually pleasing and physically accurate dynamics while preserving the dynamic details of the fine structures.

Fullscreen Image

BibTeX

@misc{feng2024elastogen,
    title={ElastoGen: 4D Generative Elastodynamics}, 
    author={Yutao Feng and Yintong Shang and Xiang Feng and Lei Lan and Shandian Zhe and Tianjia Shao and Hongzhi Wu and Kun Zhou and Hao Su and Chenfanfu Jiang and Yin Yang},
    year={2024},
    eprint={2405.15056},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}