Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains

2024-10-12

ACM Transactions on Graphics

AI Summary

Efficient, robust, and differentiable elastic simulation of implicit-function-defined deformable domains remains challenging for 3D reconstruction and physics-driven editing. Method: We propose the first end-to-end differentiable elastic simulator. It introduces a novel neural integration network to approximate physical quantities at integration points on implicit grid cells, combined with a hybrid finite element formulation and differentiable rendering—enabling fully differentiable modeling of implicit surface evolution to elastic response without explicit meshing. Contribution/Results: (1) Enables joint gradient-based optimization of geometry and material parameters; (2) supports forward elastic simulation of implicit geometries and real-time interactive editing; (3) significantly improves accuracy and convergence speed within a reconstruction–simulation–optimization closed loop. Experiments demonstrate superior physical consistency, robustness, and computational efficiency compared to prior approaches.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision
• Intelligent Robots: Embodied AI

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it is increasingly effective to recover geometry from observed images as implicit functions, but physical applications require accurately simulating and optimizing-for the behavior of such shapes under deformation, which has remained challenging. Our key technical innovation is to train a small neural network to fit quadrature points for robust numerical integration on implicit grid cells. When coupled with a Mixed Finite Element formulation, this yields a smooth, fully differentiable simulation model connecting the evolution of the underlying implicit surface to its elastic response. We demonstrate the efficacy of our approach on forward simulation of implicits, direct simulation of 3D shapes during editing, and novel physics-based shape and topology optimizations in conjunction with differentiable rendering.

Problem

• Simulating elastic behavior on evolving implicit domains
• Differentiable elasticity for shape and material optimization
• Robust integration on implicit grids via neural networks

Innovation

• Neural network for robust quadrature points
• Mixed Finite Element differentiable model
• Differentiable elasticity on evolving domains