Source-linked AI summary
Learning Implicit Constitutive Laws for Dynamic 3D Gaussian Splatting from Monocular Videos
Xiaoyang Liu, Kai Han
TL;DR
Learning intrinsic constitutive laws from monocular dynamic video is difficult because single-view geometry is ambiguous and material parameters are underconstrained. GCA combines LoRA-based adaptation with rank-based depth-geometric anchors and soft constitutive priors, achieving 48% lower Chamfer Distance than the strongest baseline on synthetic data while remaining robust across other evaluated settings.
Problem
Learning intrinsic physical dynamics from a single fixed-viewpoint video is ill-posed because monocular geometry is ambiguous and constitutive parameters are underconstrained.
Method
GCA unifies LoRA-based adaptation with RDGA for scale-invariant rank-based depth alignment and CPR for soft regularization from classical constitutive models.
Results
48% lower Chamfer Distance than the strongest baseline on synthetic data, with strong real-to-sim generalization, superior real-world visual quality, and accurate law-level recovery.
Takeaways & Limitations
GCA remains effective when the true material is absent from the constitutive hypotheses, preserving implicit-model flexibility while using physical guidance.
Abstract
from arXiv · showhide
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.
1 Introduction
GCA addresses the ill-posed problem of learning intrinsic constitutive laws from a single fixed-viewpoint deformation video by combining robust geometric alignment with soft physical priors. Experiments report stronger performance across synthetic, real-to-sim, and real-world settings.
- Motivation: Learning precise intrinsic physical models from visual signals remains an open challenge despite their importance for spatial intelligence.Such models support accurate digital modeling, interaction, and manipulation that follows physical laws.
- Problem: Existing explicit and implicit approaches offer complementary trade-offs, motivating a method that preserves implicit generalization while improving monocular reliability.The supplied related-work passage introduces predefined constitutive models as the explicit paradigm, while the core question targets reliable monocular learning with implicit modeling advantages.
- Problem: Monocular dynamic video makes constitutive-law learning ill-posed because a single viewpoint creates geometric ambiguity while physical parameters remain underconstrained.The framework assumes a static multi-view orbital scan for initial 3D geometry reconstruction.
- GCA: GCA combines LoRA-based adaptation with RDGA, which uses scale-invariant rank-based depth alignment, and CPR, which treats classical constitutive models as soft priors.RDGA reduces reliance on unreliable pixel-level color supervision, while CPR remains effective even when the true material is absent from the hypotheses.
- Results: 48% lower Chamfer Distance than NeuMA on synthetic benchmarks is reported alongside robust real-to-sim performance and superior visual quality in real-world monocular experiments.The experiments also report that naively adapting explicit methods to monocular settings can lead to optimization divergence.
2 Related work
Physics-grounded dynamic 3D generation has progressed from predefined material assumptions toward neural constitutive laws learned from observations. GCA is positioned as combining explicit-law stability with implicit-model generalization under sparse supervision.
- Prior approaches: NeRF-, Gaussian-, and diffusion-guided approaches commonly rely on predefined or imprecise material assumptions, including explicit spring-mass or rigid and elastic body models.SpringGaus reconstructs elastic dynamics with an explicit spring-mass model, while diffusion-guided methods inherit imprecise physics priors.
- Implicit modeling: NeuMA optimizes neural constitutive laws without predefined laws, but single-modality visual optimization suffers from local minima under sparse supervision.The passage positions this limitation as motivating additional priors and alignment mechanisms.
- GCA: GCA aims to unify the stability of explicit laws with the generalization of implicit ones under sparse supervision.
3 Method
GCA learns implicit constitutive laws by coupling a differentiable elastoplastic dynamical system with LoRA adaptation, geometric alignment, and constitutive priors. RDGA addresses monocular geometric ambiguity, while CPR regularizes material-law learning using candidate physical models.
- Neural material constitutive laws: GCA represents dynamics with a discrete state transition Mθ that advances particle positions, velocities, and elastic deformation gradients.The underlying continuum model uses elastoplastic dynamics, and Mθ is obtained by discretizing the governing equation.
- Neural material constitutive laws: LoRA fine-tunes neural elasticity and plasticity laws around a basic physical prior instead of training all model parameters.The model combines neural elasticity, semi-implicit Euler integration, and neural plasticity, with learned updates added to the prior laws.
- Rank-based depth-geometric anchors: RDGA replaces unreliable pixel-level supervision with scale-invariant rank-based depth alignment and stable interior correspondences.The pipeline uses rendered depth, estimated relative depth, feature correspondences, and neighborhood rank consensus to filter geometric anchors.
- Rank-based depth-geometric anchors: The geometric objective combines global point-set consistency with local anchor-level supervision based on verified Spearman rank correlations.The global term aligns matched rendered and reference point sets, while the local term emphasizes precise relationships among retained anchor pairs.
- Constitutive prior regularizer: CPR evaluates elastic and plastic constitutive hypotheses through parameter stability, assigns inverse-variance credibility weights, and penalizes weighted physical residuals.Candidate sets include four elastic models and four plasticity models; the regularizer operates alongside simulation and neural constitutive updates.
4 Experiments
GCA is evaluated on synthetic, real-to-sim, and real-world datasets, where it improves physical alignment, rendering quality, law recovery, robustness, and efficiency under monocular supervision. Ablations and stress tests attribute these gains to its alignment components and show advantages over explicit methods and full fine-tuning.
- Synthetic evaluation: 48% lower average Chamfer Distance than NeuMA is achieved on the synthetic benchmark across diverse materials.The benchmark includes six material types, varied geometries, randomized lighting, reduced frame rates, and compound materials.
- Synthetic evaluation: GCA maintains lower Chamfer Distance throughout simulation and remains aligned with ground truth as baselines gradually deviate.Synthetic rendering metrics also show superior PSNR, SSIM, and LPIPS.
- Real-to-sim evaluation: GCA achieves the lowest Chamfer Distance across all objects in the real-to-sim dataset and captures plausible dynamics for complex real-world geometries.The real-to-sim evaluation uses geometries derived from real objects with simulated dynamic sequences and ground-truth physics.
- Real-world evaluation: Under strictly single-view video supervision, GCA disentangles implicit physical properties and generalizes strongly on the SpringGaus real-world dataset.The real-world qualitative comparison reports better visual consistency; PSNR and LPIPS are computed after background filtering.
- Ablation and analysis: Rank-based depth alignment, RDGA, global alignment, and CPR each improve performance, while removing global alignment causes optimization divergence.Replacing rank-based depth loss with L1 yields average CD 0.844 versus 0.496 for the full model, and CPR improves performance on 5 of 6 materials.
- Efficiency and robustness: 60% lower GPU memory and 87% lower training time are achieved by LoRA versus full fine-tuning, alongside superior CD of 0.50 versus 1.35.Explicit PAC-NeRF becomes unstable and diverges with monocular depth supervision, reaching CD > 100, whereas GCA remains robust.
- Law recovery and generalization: 8.0% average constitutive response error versus 39.6% for NeuMA shows more accurate law-level recovery on held-out deformation gradients.GCA also outperforms baselines when the correct constitutive hypothesis is absent and for composite materials.
5 Conclusion
GCA learns implicit constitutive laws from monocular dynamic video through visual-physical alignment, achieving strong performance across synthetic, real-to-sim, and real-world evaluations while retaining defined scope boundaries.
- GCA unifies LoRA-based adaptation with RDGA and CPR for learning implicit constitutive laws from monocular dynamic video.RDGA provides geometric alignment, while CPR incorporates constitutive models as priors.
- 48% lower Chamfer Distance than the strongest baseline on synthetic data, alongside strong real-to-sim generalization and superior real-world monocular quality.
- GCA remains robust when the true material is absent from the hypotheses.
- Limitations: GCA requires a static multi-view scan for geometric initialization, so fully monocular reconstruction remains future work.
- Limitations: Geometric anchors depend on monocular depth quality, although their rank-based formulation mitigates scale-shift ambiguity.
- Limitations: Current experiments focus mainly on single-object dynamics, leaving dense multi-object scenes with heterogeneous materials for future investigation.