Problem
Research questions and friction points this paper is trying to address.
3D Gaussian Splatting
solid mechanics
inverse analysis
parameter identification
deformable solids
A differentiable Lagrangian-coupled 3D Gaussian Splatting-SPH model for forward simulation and inverse analysis in solid mechanics
🤖 AI Summary
This study addresses the limitation of 3D Gaussian Splatting (3DGS) in supporting mechanical interpretation and parameter inversion by proposing a differentiable Lagrangian coupling model that deeply integrates Smoothed Particle Hydrodynamics (SPH) physical simulation with 3DGS rendering. The core innovation lies in introducing an envelope-based SPH support generation mechanism and a reference-configuration Lagrangian mapping, which effectively decouple rendering primitives from mechanical particles to establish a unified framework for forward simulation and inverse analysis. Experimental results demonstrate that the proposed model achieves high accuracy across diverse constitutive responses and successfully recovers material parameters directly from image data, significantly outperforming conventional methods.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
3D Gaussian Splatting
Smoothed Particle Hydrodynamics
Differentiable simulation
Inverse analysis
Solid mechanics
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