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

We present GCA (Gaussian Constitutive Alignment), a frame-work for learning implicit constitutive laws from monocular dynamicvideo of deformable objects represented by 3D Gaussians. Given a staticmulti-view scan for geometric initialization, our method learns intrin-sic physical dynamics solely from a single fixed-viewpoint video of themoving object. Existing implicit methods often suffer from local minimaunder noisy supervision and lack physical interpretability, while explicitapproaches rely on predefined constitutive equations, limiting generaliz-ability and becoming unstable in monocular settings. To address thesechallenges, our framework unifies LoRA-based adaptation with two keyalignment modules. First, we propose Rank-based Depth-Geometric An-chors (RDGA) to establish robust geometric constraints from monoc-ular dynamic observations via scale-invariant rank-based depth align-ment, reducing the reliance on unreliable pixel-level color supervision.Second, a Constitutive Prior Regularizer (CPR) integrates classical con-stitutive models as soft differentiable priors, regularizing the optimiza-tion while preserving the flexibility of implicit modeling—even when theactual material is absent from the hypotheses. Extensive experiments onsynthetic, real-to-sim, and real-world datasets demonstrate that GCAoutperforms existing methods, achieving 48% lower Chamfer Distancethan the strongest baseline on synthetic benchmarks while remainingrobust under monocular supervision.