Driving · 2026-10-06
A differentiable Lagrangian-coupled 3D Gaussian Splatting-SPH model for forward simulation and inverse analysis in solid mechanics
Tian Xu, Soroush Atashi, Tianju Xue
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TL;DR
The authors propose a differentiable Lagrangian-coupled 3D Gaussian Splatting–SPH model for forward simulation and inverse analysis of deformable solids. They reconstruct a 3DGS model from multi-view calibrated images, generate an independent SPH support from the Gaussian geometry, transfer SPH deformation to Gaussian centers/covariances via a Lagrangian mapping, render differentiable deformation frames, and use the same pipeline for gradient-based parameter identification from images (including noisy cases).
Why it matters
The work aims to connect image-based 3D Gaussian representations to physically interpretable, differentiable solid mechanics models. By coupling corrected solid SPH (with elastic/hyperelastic/viscoelastic constitutive laws and fixed/free/Robin boundaries) to 3DGS rendering through a reference-configuration Lagrangian transfer, it supports both accurate forward deformation rendering and inverse estimation of constitutive and boundary parameters from rendered deformation observations.
Method
- Reconstruct a 3DGS rendering model from multi-view calibrated images; represent the visible object surface with anisotropic Gaussians (centers, covariances, opacities, appearance coefficients).
- Generate a volumetric SPH reference domain using an envelope-based procedure (voxel shell closing + filling; occupied grid-cell centers become SPH supports), avoiding direct use of rendering primitives as mechanical particles.
- Simulate with corrected total-Lagrangian solid SPH (linear elastic / neo-Hookean hyperelastic / Kelvin–Voigt viscosity; Dirichlet/Neumann/Robin-like boundary conditions), then transfer SPH motion to Gaussian centers/covariances via a differentiable reference-configuration Lagrangian SPH–GS transfer; render and use gradients for inverse parameter estimation in JAX.
Abstract (from 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.
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Publication record
Bibliographic evidence describes where and when a record appeared. It does not validate scientific claims.
First public release: 2026-10-03 · Indexed by Pub-AI: 2026-10-06 UTC
A differentiable Lagrangian-coupled 3D Gaussian Splatting-SPH model for forward simulation and inverse analysis in solid mechanics
Preprint posted: 2026-10-03 · Original record ↗
- arxiv
- 2610.04336
Explicit source versions (1)
- v1 · 2026-10-03
- Preprint available
Source date: 2026-10-03 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
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.