# Neural Stress Fields for Reduced-order Elastoplasticity and Fracture

arXiv: https://arxiv.org/abs/2310.17790 · HTML: https://mlsanity.com/paper/2310.17790/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 68 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Implicit Neural Spatial Representations for Time-dependent PDEs](https://mlsanity.com/paper/2210.00124/) (2022)
- [High-order Differentiable Autoencoder for Nonlinear Model Reduction](https://mlsanity.com/paper/2102.11026/) (2021)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [Model reduction for the material point method via an implicit neural representation of the deformation map](https://mlsanity.com/paper/2109.12390/) (2021)
- [Hierarchical Optimization Time Integration for CFL-rate MPM Stepping](https://mlsanity.com/paper/1911.07913/) (2019)
- [Principles towards Real-Time Simulation of Material Point Method on Modern GPUs](https://mlsanity.com/paper/2111.00699/) (2021)

## Built on by (most cited first, 24 of 24)

- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [VideoPhy: Evaluating Physical Commonsense for Video Generation](https://mlsanity.com/paper/2406.03520/) (2024)
- [PhysMotion: Physics-Grounded Dynamics From a Single Image](https://mlsanity.com/paper/2411.17189/) (2024)
- [PhysFlow: Unleashing the Potential of Multi-modal Foundation Models and Video Diffusion for 4D Dynamic Physical Scene Simulation](https://mlsanity.com/paper/2411.14423/) (2024)
- [Neural Material Adaptor for Visual Grounding of Intrinsic Dynamics](https://mlsanity.com/paper/2410.08257/) (2024)
- [Neural Fields in Robotics: A Survey](https://mlsanity.com/paper/2410.20220/) (2024)
- [DecoupledGaussian: Object-Scene Decoupling for Physics-Based Interaction](https://mlsanity.com/paper/2503.05484/) (2025)
- [Physical Simulator In-the-Loop Video Generation](https://mlsanity.com/paper/2603.06408/) (2026)
- [VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models](https://mlsanity.com/paper/2506.13754/) (2025)
- [Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization](https://mlsanity.com/paper/2409.03807/) (2024)
- [SOPHY: Learning to Generate Simulation-Ready Objects with Physical Materials](https://mlsanity.com/paper/2504.12684/) (2025)
- [PhyMAGIC: Physical Motion-Aware Generative Inference with Confidence-guided LLM](https://mlsanity.com/paper/2505.16456/) (2025)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [Realistic Surgical Simulation from Monocular Videos](https://mlsanity.com/paper/2412.02359/) (2024)
- [Tube Diffusion Policy: Reactive Visual-Tactile Policy Learning for Contact-rich Manipulation](https://mlsanity.com/paper/2604.23609/) (2026)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [Data-Driven Nonlinear Deformation Design of 3D-Printable Shells](https://mlsanity.com/paper/2408.15097/) (2024)
- [Gaussian Swaying: Surface-Based Framework for Aerodynamic Simulation with 3D Gaussians](https://mlsanity.com/paper/2512.01306/) (2025)
- [PhysSkin: Real-Time and Generalizable Physics-Based Animation via Self-Supervised Neural Skinning](https://mlsanity.com/paper/2603.23194/) (2026)
- [Reduced-order Neural Modeling with Differentiable Simulation for High-Detail Tactile Perception](https://mlsanity.com/paper/2605.05053/) (2026)
- [Fishbone: From One 3D Asset to a Million Controllable Edits](https://mlsanity.com/paper/2605.24805/) (2026)
- [MeGAS: Thermomechanical Dynamic Gaussian Splatting for Thermophysical Scene Editing](https://mlsanity.com/paper/2606.23455/) (2026)
- [Neural Voxel Dynamics: Learning Volumetric Feature Advection for 3D Physics in V-JEPA Latent Space](https://mlsanity.com/paper/2606.26410/) (2026)
- [FracGen: Learning How Objects Stretch and Tear with Physics-Informed Video Generation](https://mlsanity.com/paper/2609.38152/) (2026)

## Abstract (arXiv)

We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation elastoplasticity and fracture mechanics. However, their long runtime and large memory consumption render them unsuitable for applications constrained by computation time and memory usage, e.g., virtual reality. To overcome these barriers, we propose a reduced-order framework. Our key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. This low-dimensional neural stress field (NSF) enables efficient evaluations of stress values and, correspondingly, internal forces at arbitrary spatial locations. In addition, we also train neural deformation and affine fields to build low-dimensional manifolds for the deformation and affine momentum fields. These neural stress, deformation, and affine fields share the same low-dimensional latent space, which uniquely embeds the high-dimensional simulation state. After training, we run new simulations by evolving in this single latent space, which drastically reduces the computation time and memory consumption. Our general continuum-mechanics-based reduced-order framework is applicable to any phenomena governed by the elastodynamics equation. To showcase the versatility of our framework, we simulate a wide range of material behaviors, including elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision. We demonstrate dimension reduction by up to 100,000X and time savings by up to 10X.