ElastoGen: 4D Generative Elastodynamics

TL;DR

ElastoGen introduces a physics-informed, lightweight generative model for coherent 4D elastodynamics by translating nonlinear force equilibrium into local, convolution-like relaxation steps. Its core innovations include NeuralMTL for material-aware local energy corrections, a diffusion-driven parameter generator for material constants, and a two-level RNN with subspace encoding to enable efficient global relaxation without large data requirements. Empirical results show close alignment with FEM across multiple hyperelastic materials and strong advantage over observation-based 4D models in both physical fidelity and geometric consistency. The approach offers a practical pathway for end-to-end 4D generation that integrates with upstream 3D generators and downstream modules while reducing training burdens. Limitations include collision handling and performance on extremely stiff or thin geometries, guiding future enhancements in broader physical phenomena and robustness.

Abstract

We present ElastoGen, a knowledge-driven AI model that generates physically accurate 4D elastodynamics. Unlike deep models that learn from video- or image-based observations, ElastoGen leverages the principles of physics and learns from established mathematical and optimization procedures. The core idea of ElastoGen is converting the differential equation, corresponding to the nonlinear force equilibrium, into a series of iterative local convolution-like operations, which naturally fit deep architectures. We carefully build our network module following this overarching design philosophy. ElastoGen is much more lightweight in terms of both training requirements and network scale than deep generative models. Because of its alignment with actual 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.

Figures (11)

• Figure 1: Pipeline overview.(a) ElastoGen rasterizes an input 3D model (with boundary conditions) and generates parameters filling our NeuralMTL module. Conceptually, NeuralMTL predicts locally concentrated strain of the object, which is relaxed by a nested RNN loop. (b) The RNN predicts the future trajectory of the object. There are two sub RNN modules. RNN-1 repeatedly relaxes the local stress in a 3D convolution manner. Those relaxed strains are converted to positional signals, and RNN-2 merges local deformation into a displacement field of the object. ElastoGen automatically checks the accuracy of the prediction of both RNN loops, and outputs the final prediction of $\mathbf{q}_{n+1}$ once the prediction error reaches the prescribed threshold.
• Figure 2: (a). NeuralMTL learns a mapping $\mathcal{N}$ to warp $\mathbf{F}_i$, enabling the quadratic strain energy to work for hyperelastic materials (b). Sampling topology over 2D input space to ensure smooth output variation. (c) Deforming object with rasterization grid.
• Figure 3: ElastoGen with implicit models. ElastoGen supports both explicit and implicit models. We dense-samples the implicit neural field, directly generating physically accurate dynamics without a simulator, enabling image-to-image generation from novel camera poses.
• Figure 4: Quantitative validation of NeuralMTL.(a) Comparison between the energy computed from NeuralMTL strain and the ground truth energy. (b) Visualization of the final static state of the cantilever beam generated by our method, with different materials and material parameters. (c) Plots of the elastic energy during the prediction.
• Figure 5: Experiments on high-resolution mesh objects. ElastoGen generates realistic nonlinear elastic dynamics under external forces. Both high-frequency local details and low-frequency global deformations are effectively captured with a carefully designed nested RNN architecture.