Title: PhyCo: Physics-Consistent Learning of Implicit Constitutive Laws via Monocular Observations of 3D Gaussians
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Gaussian splatting, physics-informed learning, implicit constitutive laws

Abstract: We present **PhyCo**, a framework for learning implicit constitutive laws from monocular observations of Gaussian splatting. 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. To address these issues, our framework, **PhyCo**, introduces two key innovations. First, we propose *Edge-Aware Depth Consensus Anchors* to establish robust geometric constraints from sparse observations, circumventing unreliable pixel-level supervision. Second, a *Multi-Hypothesis Physics Verifier* integrates classical constitutive models as differentiable hypotheses, providing strong physical priors to regularize the optimization while preserving the flexibility of implicit modeling. This unified approach ensures physical plausibility without sacrificing generality. Extensive experiments on synthetic, real-to-sim, and real-world datasets demonstrate that **PhyCo** significantly outperforms existing methods, achieving state-of-the-art performance in learning accurate and generalizable physical dynamics from monocular videos.