# A differentiable Lagrangian-coupled 3D Gaussian Splatting-SPH model for forward simulation and inverse analysis in solid mechanics

arXiv: https://arxiv.org/abs/2610.04336 · HTML: https://mlsanity.com/paper/2610.04336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Placed in

- World models

## Builds on (most cited first, 17 of 17)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [World Simulation with Video Foundation Models for Physical AI](https://mlsanity.com/paper/2511.00062/) (2025)
- [PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation](https://mlsanity.com/paper/2404.13026/) (2024)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians](https://mlsanity.com/paper/2403.09434/) (2024)
- [PhysTwin: Physics-Informed Reconstruction and Simulation of Deformable Objects from Videos](https://mlsanity.com/paper/2503.17973/) (2025)
- [OmniPhysGS: 3D Constitutive Gaussians for General Physics-Based Dynamics Generation](https://mlsanity.com/paper/2501.18982/) (2025)
- [JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science](https://mlsanity.com/paper/2212.00964/) (2022)
- [Neural Material Adaptor for Visual Grounding of Intrinsic Dynamics](https://mlsanity.com/paper/2410.08257/) (2024)
- [Efficient Physics Simulation for 3D Scenes via MLLM-Guided Gaussian Splatting](https://mlsanity.com/paper/2411.12789/) (2024)
- [GaussianFluent: Gaussian Simulation for Dynamic Scenes with Mixed Materials](https://mlsanity.com/paper/2601.09265/) (2026)
- [JAX-SPH: A Differentiable Smoothed Particle Hydrodynamics Framework](https://mlsanity.com/paper/2403.04750/) (2024)
- [TopoGaussian: Inferring Internal Topology Structures from Visual Clues](https://mlsanity.com/paper/2503.12343/) (2025)
- [PhysTalk: Language-driven Real-time Physics in 3D Gaussian Scenes](https://mlsanity.com/paper/2512.24986/) (2025)
- [MonoPhysics: Estimating Geometry, Appearance, and Physical Parameters from Monocular Videos](https://mlsanity.com/paper/2605.30320/) (2026)

## Abstract (arXiv)

Recent advances in generative world models have increased interest in digital models that reproduce both the appearance of real objects and their response to physical interaction. Three-dimensional reconstruction techniques, including 3D Gaussian Splatting, capture detailed surface geometry and appearance from images and videos. However, extending these representations beyond plausible animation to mechanically interpretable models for constitutive behavior, boundary conditions, and inverse parameter identification remains less explored. In this work, a differentiable Lagrangian-coupled 3DGS-smoothed particle hydrodynamics (SPH) model is proposed for forward simulation and inverse analysis of deformable solids. The observed object is first reconstructed from multi-view calibrated visual dataset as a 3DGS rendering model. An envelope-based procedure then generates an independent SPH support for the solid-mechanics model, avoiding the direct use of rendering primitives as mechanical particles. A reference-configuration Lagrangian transfer maps SPH deformation to Gaussian positions and covariances, thereby coupling the physical model and the image observation model while preserving a differentiable computational path. The SPH formulation supports linear elastic, hyperelastic, and Kelvin--Voigt viscoelastic responses, together with fixed, free, and Robin-type boundary conditions. Numerical studies validate the SPH response against finite-element results, assess accuracy and efficiency against a conventional model using Gaussian centers as surface SPH particles, and demonstrate forward simulations on beam, bridge, and liver-shaped examples. Inverse analyses further estimate constitutive and boundary parameters from rendered deformation observations, including noisy cases, demonstrating the feasibility of the proposed model for mechanics-based parameter identification from image data.