G-Inverse: Generative Neural Inverse Dynamics for Deformable Objects

Data-driven representations have enabled increasingly general models of deformable 3D objects. However, inferring how an object will respond to new physical interactions from a single observed motion remains challenging: the observed trajectory entangles the object's intrinsic material behavior with its initial state and external conditions. Existing inverse-physics approaches commonly recover parameters of a predefined material model by reproducing the observation, which does not necessarily yield a response model that remains valid beyond the demonstrated interaction. We introduce a generative neural inverse-physics framework that learns reusable material behavior from a single observed 4D sequence. Our method combines a pretrained neural deformation representation with a differentiable physical simulator operating in compact deformation coordinates. Within this representation, we learn a spatially shared material-response model whose evolving internal state captures deformation history, while the simulator explicitly accounts for coupled rigid and nonrigid motion, external forces, and contact. Once identified from the demonstration, the deformation representation and material model are fixed and reused to generate continuous 3D motion under new initial poses, velocities, forces, and contact conditions, without fitting to the target trajectories. This formulation turns single-sequence reconstruction into a model of object-specific physical behavior that can be queried under novel interactions.