NeuralCut: Data-Free Learning of Neural Reduced-Order Cut Simulation

Cutting deformable objects is common in daily life, but the resulting displacement discontinuities pose significant challenges for reduced-order simulation. We introduce NeuralCut, a novel data-free learning framework for reduced-order cut simulation of deformable 3D objects. NeuralCut uses neural skinning to represent full-space deformation in a compact subspace. To represent cut-induced displacement discontinuities, we develop a geometry-derived lifting-and-restriction formulation that augments spatial coordinates with a cut-dependent scalar lifting coordinate. This coordinate separates opposite sides of the cut while smoothly vanishing at its boundary, enabling discontinuous deformation across the cut and continuous deformation at the boundary. We learn the skinning fields through physics-informed self-supervision without costly full-space simulation trajectories. Our training objective minimizes expected potential energy estimated by cut-aware Monte Carlo importance sampling, promotes distinct weights across the cut through a cross-side jump constraint, and encourages orthogonality among the skinning weight functions. Experiments demonstrate real-time reduced-order cut simulation across diverse 3D objects and cut configurations, supporting both meshes and Gaussian splats. We further demonstrate NeuralCut in robot interaction simulation. Moreover, coupling NeuralCut with a transformer-based model enables cross-object generalization of cut-conditioned neural skinning.