# Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains

arXiv: https://arxiv.org/abs/2410.09417 · HTML: https://mlsanity.com/paper/2410.09417/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 80 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 26 of 26)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [LRM: Large Reconstruction Model for Single Image to 3D](https://mlsanity.com/paper/2311.04400/) (2023)
- [pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction](https://mlsanity.com/paper/2312.12337/) (2023)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [PQ-NET: A Generative Part Seq2Seq Network for 3D Shapes](https://mlsanity.com/paper/1911.10949/) (2019)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [MeshFormer: High-Quality Mesh Generation with 3D-Guided Reconstruction Model](https://mlsanity.com/paper/2408.10198/) (2024)
- [PhyRecon: Physically Plausible Neural Scene Reconstruction](https://mlsanity.com/paper/2404.16666/) (2024)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Physically Compatible 3D Object Modeling from a Single Image](https://mlsanity.com/paper/2405.20510/) (2024)
- [Differentiable solver for time-dependent deformation problems with contact](https://mlsanity.com/paper/2205.13643/) (2022)
- [Neural Metamaterial Networks for Nonlinear Material Design](https://mlsanity.com/paper/2309.10600/) (2023)
- [Differentiable Simulation of Inertial Musculotendons](https://mlsanity.com/paper/2202.02344/) (2022)
- [Topology Optimization Using Polytopes](https://mlsanity.com/paper/1312.7016/) (2013)

## Built on by (most cited first, 3 of 3)

- [ParticleGS: Learning Neural Gaussian Particle Dynamics from Videos for Prior-free Physical Motion Extrapolation](https://mlsanity.com/paper/2505.20270/) (2025)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)

## Abstract (arXiv)

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.