arXiv:2610.04689v2 Announce Type: replace Abstract: Time integration has been the cornerstone of physics-based animation that enables the simulation of complex interactions between rigid and deformable objects, including the motion of hair. Despite recent advances with optimized time integration that enabled thousands of hair strands to be simulated in real time, achieving the same performance on commodity hardware remains infeasible due to the computational demands of resolving complex dynamics and interactions between thousands of individual strands. With the rise of learning-based techniques, the offload of time integration to neural networks helps to achieve significant performance gains, making these approaches suitable for real-time applications such as gaming and virtual avatars. However, state-of-the-art neural techniques tend to produce less physically plausible motion and oftentimes fail to generalize to out-of-distribution scenarios. Inspired by classical time integrators, we design a neural counterpart that mirrors their input-output formulation -- taking previous hair states, material stiffness, and collision geometry as the inputs for the neural time integrator, which is then trained via a self-supervised, simulator-in-the-loop method with randomized unrolling horizons. By formulating training in each strand's local coordinate frame, we obtain a network that generalizes across multiple dimensions, including hairstyle, material property, body motion, and body type. Our method inherits the benefits of a strand-based neural simulator, and hence is density-independent, lightweight, memory-efficient, and performant. Our neural hair integrator produces stable long-horizon rollouts and can be naturally extended to support quasi-static simulation simply by resetting hair states.