# Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation

arXiv: https://arxiv.org/abs/2407.09497 · HTML: https://mlsanity.com/paper/2407.09497/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 63 references that are in the map.
- First posted on arXiv 9 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [SCANimate: Weakly Supervised Learning of Skinned Clothed Avatar Networks](https://mlsanity.com/paper/2104.03313/) (2021)
- [LEAP: Learning Articulated Occupancy of People](https://mlsanity.com/paper/2104.06849/) (2021)
- [PIE-NeRF: Physics-based Interactive Elastodynamics with NeRF](https://mlsanity.com/paper/2311.13099/) (2023)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [VolTeMorph: Realtime, Controllable and Generalisable Animation of Volumetric Representations](https://mlsanity.com/paper/2208.00949/) (2022)
- [Codimensional Incremental Potential Contact](https://mlsanity.com/paper/2012.04457/) (2020)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [Fast Complementary Dynamics via Skinning Eigenmodes](https://mlsanity.com/paper/2303.11886/) (2023)
- [Constrained Delaunay Tetrahedrization: A Robust and Practical Approach](https://mlsanity.com/paper/2309.09805/) (2023)
- [Poly-Spline Finite Element Method](https://mlsanity.com/paper/1804.03245/) (2018)

## Built on by (most cited first, 27 of 27)

- [PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation](https://mlsanity.com/paper/2509.20358/) (2025)
- [Efficient Physics Simulation for 3D Scenes via MLLM-Guided Gaussian Splatting](https://mlsanity.com/paper/2411.12789/) (2024)
- [Make-It-Animatable: An Efficient Framework for Authoring Animation-Ready 3D Characters](https://mlsanity.com/paper/2411.18197/) (2024)
- [Vid2Sim: Generalizable, Video-based Reconstruction of Appearance, Geometry and Physics for Mesh-free Simulation](https://mlsanity.com/paper/2506.06440/) (2025)
- [DecoupledGaussian: Object-Scene Decoupling for Physics-Based Interaction](https://mlsanity.com/paper/2503.05484/) (2025)
- [Triangle Splatting+: Differentiable Rendering with Opaque Triangles](https://mlsanity.com/paper/2509.25122/) (2025)
- [ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimation](https://mlsanity.com/paper/2506.05317/) (2025)
- [Gaussian-Augmented Physics Simulation and System Identification with Complex Colliders](https://mlsanity.com/paper/2511.06846/) (2025)
- [WorldParticle: Unified World Simulation of Lagrangian Particle Dynamics via Transformer](https://mlsanity.com/paper/2605.15305/) (2026)
- [MonoPhysics: Estimating Geometry, Appearance, and Physical Parameters from Monocular Videos](https://mlsanity.com/paper/2605.30320/) (2026)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [Axolotl3D: a Unified Framework for Faithful 3D Shape Completion](https://mlsanity.com/paper/2607.20660/) (2026)
- [Low-Rank Adaptation of Neural Fields](https://mlsanity.com/paper/2504.15933/) (2025)
- [ArtisanGS: Interactive Tools for Gaussian Splat Selection with AI and Human in the Loop](https://mlsanity.com/paper/2602.10173/) (2026)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [NewtPhys: Do Foundation Models Understand Newtonian Physics?](https://mlsanity.com/paper/2606.03986/) (2026)
- [UniPixie: Unified and Probabilistic 3D Physics Learning via Flow Matching](https://mlsanity.com/paper/2606.05399/) (2026)
- [Adaptive Volumetric Mechanical Property Fields Invariant to Resolution](https://mlsanity.com/paper/2606.18231/) (2026)
- [Learning the Right Abstraction: Neural Reduced Dynamics for Complex Robot Control](https://mlsanity.com/paper/2608.19375/) (2026)
- [Snap-and-tune: combining deep learning and test-time optimization for high-fidelity cardiovascular volumetric meshing](https://mlsanity.com/paper/2506.08280/) (2025)
- [Generalized Dynamics Generation towards Scannable Physical World Model](https://mlsanity.com/paper/2510.15041/) (2025)
- [PhysSkin: Real-Time and Generalizable Physics-Based Animation via Self-Supervised Neural Skinning](https://mlsanity.com/paper/2603.23194/) (2026)
- [Learning Orthonormal Bases for Function Spaces](https://mlsanity.com/paper/2605.19959/) (2026)
- [HyperBones: Realtime Bone-driven Neural Garment Simulation with Hypernetwork Conditioning](https://mlsanity.com/paper/2605.20460/) (2026)
- [MoSA: Motion-constrained Stress Adaptation for Mitigating Real-to-Sim Gap in Continuum Dynamics via Learning Residual Anisotropy](https://mlsanity.com/paper/2605.22597/) (2026)
- [TRON: Tracing Rays to Orchestrate a Neural Renderer for 3D Gaussian Reconstructions](https://mlsanity.com/paper/2606.11314/) (2026)
- [RealSimLoop: Online Real-to-Sim Adaptation via Differentiable Reduced-Order Simulation with Vision Feedback](https://mlsanity.com/paper/2609.09828/) (2026)

## Abstract (arXiv)

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. 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, as well as showing a variety of material energies, contact models, and time integration schemes.