# Learning Implicit Constitutive Laws for Dynamic 3D Gaussian Splatting from Monocular Videos

arXiv: https://arxiv.org/abs/2608.22102 · HTML: https://mlsanity.com/paper/2608.22102/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Builds on (most cited first, 30 of 35)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [R3M: A Universal Visual Representation for Robot Manipulation](https://mlsanity.com/paper/2203.12601/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation](https://mlsanity.com/paper/2404.13026/) (2024)
- [VR-GS: A Physical Dynamics-Aware Interactive Gaussian Splatting System in Virtual Reality](https://mlsanity.com/paper/2401.16663/) (2024)
- [PhysGen: Rigid-Body Physics-Grounded Image-to-Video Generation](https://mlsanity.com/paper/2409.18964/) (2024)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians](https://mlsanity.com/paper/2403.09434/) (2024)
- [Generative Image Dynamics](https://mlsanity.com/paper/2309.07906/) (2023)
- [Physics3D: Learning Physical Properties of 3D Gaussians via Video Diffusion](https://mlsanity.com/paper/2406.04338/) (2024)
- [OmniPhysGS: 3D Constitutive Gaussians for General Physics-Based Dynamics Generation](https://mlsanity.com/paper/2501.18982/) (2025)
- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [Depth Any Video with Scalable Synthetic Data](https://mlsanity.com/paper/2410.10815/) (2024)
- [PIE-NeRF: Physics-based Interactive Elastodynamics with NeRF](https://mlsanity.com/paper/2311.13099/) (2023)
- [GIC: Gaussian-Informed Continuum for Physical Property Identification and Simulation](https://mlsanity.com/paper/2406.14927/) (2024)
- [MotionCraft: Physics-based Zero-Shot Video Generation](https://mlsanity.com/paper/2405.13557/) (2024)
- [PhysMotion: Physics-Grounded Dynamics From a Single Image](https://mlsanity.com/paper/2411.17189/) (2024)
- [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)
- [Gaussian Splashing: Unified Particles for Versatile Motion Synthesis and Rendering](https://mlsanity.com/paper/2401.15318/) (2024)
- [Virtual Elastic Objects](https://mlsanity.com/paper/2201.04623/) (2022)

## Abstract (arXiv)

We present GCA (Gaussian Constitutive Alignment), a framework for learning implicit constitutive laws from monocular dynamic video of deformable objects represented by 3D Gaussians. Given a static multi-view scan for geometric initialization, our method learns intrinsic physical dynamics solely from a single fixed-viewpoint video of the moving object. Existing implicit methods often suffer from local minima under noisy supervision and lack physical interpretability, while explicit approaches rely on predefined constitutive equations, limiting generalizability and becoming unstable in monocular settings. To address these challenges, our framework unifies LoRA-based adaptation with two key alignment modules. First, we propose Rank-based Depth-Geometric Anchors (RDGA) to establish robust geometric constraints from monocular dynamic observations via scale-invariant rank-based depth alignment, reducing the reliance on unreliable pixel-level color supervision. Second, a Constitutive Prior Regularizer (CPR) integrates classical constitutive models as soft differentiable priors, regularizing the optimization while preserving the flexibility of implicit modeling---even when the actual material is absent from the hypotheses. Extensive experiments on synthetic, real-to-sim, and real-world datasets demonstrate that GCA outperforms existing methods, achieving 48% lower Chamfer Distance than the strongest baseline on synthetic benchmarks while remaining robust under monocular supervision.