ElastoGen: 4D Generative Elastodynamics

2024-05-23

arXiv.org

AI Summary

This work addresses the longstanding challenge of balancing physical fidelity and computational efficiency in four-dimensional (3D spatial + temporal) elastodynamic simulation of hyperelastic materials. We propose a physics-knowledge-driven lightweight neural network method. Its core innovation lies in explicitly encoding the nonlinear elastic force-balance partial differential equations as learnable local iterative convolutional operators, thereby achieving native integration of first-principles physics into deep network architecture. The method operates without video or image supervision and generates high-fidelity 4D dynamic sequences end-to-end. It features minimal parameter count, low training overhead, strong generalization across diverse hyperelastic material models, and seamless compatibility with downstream deep learning pipelines—enabling real-time simulation.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

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.

Problem

• Generates physically accurate 4D elastodynamics using physics principles
• Converts nonlinear force equilibrium equations into iterative convolution operations
• Enables efficient 4D generation for hyperelastic materials with lightweight architecture

Innovation

• Converts force equilibrium equations into iterative convolutions
• Leverages physics principles instead of visual data
• Lightweight network aligned with physical optimization procedures