Cloth dynamics leaves the fixed timestep behind: ContinuousCloth writes motion as a continuous function of time and evaluates dense trajectories up to 17.4x faster
Synopsis
Cloth simulators usually cut motion into fixed timesteps and return states only on the solver grid, so querying arbitrary times or derivatives means re-running or finite differences. ContinuousCloth represents the cloth trajectory as a differentiable function of time, trained under the residual of a spring-mass ordinary differential equation, and answers position and derivative queries at any timestamp. Across six boundary-condition scenarios its trajectory accuracy matches a high-precision fourth-order Runge-Kutta reference while dense-time evaluation runs up to 17.4 times faster.
Interpretation
Cloth motion can now be written as a trajectory that is continuous and differentiable in time, rather than states returned only on a solver-defined discrete time grid. Classical cloth simulators cut motion into timesteps and return states only at grid points; coarse steps accumulate error and can diverge, while smaller steps raise computational cost proportionally. Across six boundary-condition scenarios, compared with a fourth-order Runge-Kutta reference using a small timestep, both ContinuousCloth-MLP and ContinuousCloth-Former keep low physics residuals and trajectory RMSE, and trajectory overlays show temporal alignment with the reference and no visible drift.
A trained network produces the whole trajectory in a single forward pass, so query cost no longer grows with temporal resolution. Fourth-order Runge-Kutta cost scales linearly with the number of integration steps, whereas the continuous trajectory field decouples evaluation from a fixed integration grid. Averaged over the six scenarios per rollout, both ContinuousCloth-MLP and ContinuousCloth-Former take less time than fourth-order Runge-Kutta, and the conclusion reports a dense-time evaluation speedup of up to 17.4x.
The same formulation also acts as a physical prior for trajectory interpolation and inverse parameter estimation when observations are sparse and noisy. A data-only neural network can fit sparse measurements but often lacks temporal consistency and overfits noise, while a simulator-based differentiable solver absorbs noise directly into parameter estimates. Training on every 10th frame and reconstructing intermediate frames in simulation, ContinuousCloth-MLP beats the data-only MLP baseline in both the clean and high-noise settings; under high noise its relative parameter error is lower than the differentiable fourth-order Runge-Kutta baseline, and its held-out RMSE is lower on all three real fabrics.
Perspective
The demonstrated scope is the spring-mass cloth model: data-free forward simulation in six static and moving boundary-condition scenarios, plus interpolation and parameter estimation in simulation and on three real cloth sequences; the real data were recorded with a ZED2i camera, tracking 90 points over 50 frames per scenario. The current model does not yet handle contact-rich scenarios such as collision, self-contact and friction, and the authors list extending to these settings as future work.
Several numbers in the text appear as placeholders, such as the magnitudes of physics residuals, some RMSE values and the camera frame rate, so those comparisons can only be read for direction. Real-cloth physical parameters are unknown and must first be estimated by inverse fitting before interpolation; the real-world parameter-estimation evaluation uses a cross-condition setup trained on the Fling scenario and transferred to the Shaking scenario.