Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains

• URL: http://arxiv.org/abs/2410.09417v1
• Date: Sat, 12 Oct 2024 07:49:23 GMT
• Title: Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains
• Authors: Gilles Daviet, Tianchang Shen, Nicholas Sharp, David I. W. Levin,
• Abstract summary: elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to shape and material. Key technical innovation is to train a small neural network to fit quadrature points for robust numerical integration on implicit grid cells. 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.
• Score: 19.755626638375904
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation [60.33467489955188]
  This paper studies the problem of estimating physical properties (system identification) through visual observations. To facilitate geometry-aware guidance in physical property estimation, we introduce a novel hybrid framework. We propose a new dynamic 3D Gaussian framework based on motion factorization to recover the object as 3D Gaussian point sets. In addition to the extracted object surfaces, the Gaussian-informed continuum also enables the rendering of object masks during simulations.
  arXiv  Detail & Related papers  (2024-06-21T07:37:17Z)
• Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation [18.45850302604534]
  We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation. For each object, we fit a small implicit neural network encoding varying weights that act as a reduced deformation basis. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes.
  arXiv  Detail & Related papers  (2024-06-09T18:57:23Z)
• Physically Compatible 3D Object Modeling from a Single Image [109.98124149566927]
  We present a framework that transforms single images into 3D physical objects. Our framework embeds physical compatibility into the reconstruction process. It consistently enhances the physical realism of 3D models over existing methods.
  arXiv  Detail & Related papers  (2024-05-30T21:59:29Z)
• PhyRecon: Physically Plausible Neural Scene Reconstruction [81.73129450090684]
  We introduce PHYRECON, the first approach to leverage both differentiable rendering and differentiable physics simulation to learn implicit surface representations. Central to this design is an efficient transformation between SDF-based implicit representations and explicit surface points. Our results also exhibit superior physical stability in physical simulators, with at least a 40% improvement across all datasets.
  arXiv  Detail & Related papers  (2024-04-25T15:06:58Z)
• PIE-NeRF: Physics-based Interactive Elastodynamics with NeRF [29.6350855891474]
  We show that physics-based simulations can be seamlessly integrated with NeRF to generate high-quality elastodynamics of real-world objects. A quadratic generalized moving least square (Q-GMLS) is employed to capture nonlinear dynamics and large deformation on the implicit model. We adaptively place the least-square kernels according to the NeRF density field to significantly reduce the complexity of the nonlinear simulation.
  arXiv  Detail & Related papers  (2023-11-22T01:58:26Z)
• Flexible Isosurface Extraction for Gradient-Based Mesh Optimization [65.76362454554754]
  This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives.
  arXiv  Detail & Related papers  (2023-08-10T06:40:19Z)
• Physics-informed UNets for Discovering Hidden Elasticity in Heterogeneous Materials [0.0]
  We develop a novel UNet-based neural network model for inversion in elasticity (El-UNet) We show superior performance, both in terms of accuracy and computational cost, by El-UNet compared to fully-connected physics-informed neural networks.
  arXiv  Detail & Related papers  (2023-06-01T23:35:03Z)
• Dynamic Point Fields [30.029872787758705]
  We present a dynamic point field model that combines the representational benefits of explicit point-based graphics with implicit deformation networks. We show the advantages of our dynamic point field framework in terms of its representational power, learning efficiency, and robustness to out-of-distribution novel poses.
  arXiv  Detail & Related papers  (2023-04-05T17:52:37Z)
• {\phi}-SfT: Shape-from-Template with a Physics-Based Deformation Model [69.27632025495512]
  Shape-from-Template (SfT) methods estimate 3D surface deformations from a single monocular RGB camera. This paper proposes a new SfT approach explaining 2D observations through physical simulations.
  arXiv  Detail & Related papers  (2022-03-22T17:59:57Z)
• NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go [109.88509362837475]
  We present NeuroMorph, a new neural network architecture that takes as input two 3D shapes. NeuroMorph produces smooth and point-to-point correspondences between them. It works well for a large variety of input shapes, including non-isometric pairs from different object categories.
  arXiv  Detail & Related papers  (2021-06-17T12:25:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.