发表机构
Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出可微拉格朗日耦合3DGS-SPH模型，实现固体力学正演模拟与从图像反演本构及边界参数，经数值验证并应用于梁、桥、肝脏示例。
AI 中文摘要
生成式世界模型的最新进展增加了人们对既能再现真实物体外观又能响应物理交互的数字模型的兴趣。包括三维高斯泼溅（3D Gaussian Splatting, 3DGS）在内的三维重建技术可从图像和视频中捕获详细的表面几何和外观。然而，将这些表示从合理的动画扩展到可机械解释的模型，以用于本构行为、边界条件和反演参数识别，仍较少被探索。在本工作中，提出了一种可微拉格朗日耦合的3DGS-光滑粒子流体动力学（smoothed particle hydrodynamics, SPH）模型，用于可变形固体的正演模拟和反演分析。首先从多视角标定视觉数据集中将观测对象重建为3DGS渲染模型。然后，基于包络的程序为固体力学模型生成独立的SPH支撑，避免直接使用渲染基元作为力学粒子。参考构型下的拉格朗日传递将SPH变形映射到高斯位置和协方差，从而将物理模型与图像观测模型耦合，同时保持可微的计算路径。SPH公式支持线弹性、超弹性和Kelvin-Voigt粘弹性响应，以及固定、自由和Robin型边界条件。数值研究将SPH响应与有限元结果进行验证，评估了相对于使用高斯中心作为表面SPH粒子的传统模型的准确性和效率，并在梁、桥和肝脏形状的示例上演示了正演模拟。反演分析进一步从渲染变形观测（包括噪声情况）中估计本构和边界参数，证明了所提出模型从图像数据中进行基于力学的参数识别的可行性。
英文摘要
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.
