cs.LGOct 9, 2026

Continuous-Time Cloth Dynamics with Physics-Informed Neural ODEs

Authors: Yingdong Ru, Lipeng Zhuang, Zhuo He, Gerardo Aragon Camarasa

Organizations: University of Glasgow, Glasgow, United Kingdom

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Abstract

We present ContinuousCloth, a continuous-time, physics-informed neural solver for deformable cloth dynamics that enforces a spring--mass ODE within a neural trajectory model. Unlike classical time-stepping simulators that return trajectories only on a discrete integration grid, ContinuousCloth supports querying at arbitrary timestamps and computing displacement, velocity, and acceleration via automatic differentiation. We evaluate ContinuousCloth along two dimensions. In a physics-only setting, ContinuousCloth achieves trajectory accuracy comparable to high-precision solvers across six diverse boundary-condition scenarios while reducing runtime by up to 17.4 times. When fused with sparse and noisy observations, the spring--mass ODE acts as a strong inductive bias for downstream tasks: interpolation and parameter estimation. That is, ContinuousCloth reduces interpolation error by 7.3 times over a data-only neural baseline in simulation and 2.4 times on real-world cloth sequences, and achieves 2.6 times lower parameter error than a differentiable-solver baseline under high-noise conditions, demonstrating consistent robustness under realistic measurement imperfections.

Figures & tables

Figure 1: (a) Classic simulators accumulate errors on discrete grids and can become unstable, whereas ContinuousCloth represents cloth motion as a continuous function queryable at any tt . (b) Given only the first and last frames, ContinuousCloth reconstructs a physically consistent trajectory across the full intermediate horizon.
Figure 2: Overview of ContinuousCloth. We represent cloth dynamics as a continuous-time trajectory field conditioned on boundary conditions and physical parameters, and enforce spring–mass ODE constraints via physics residuals computed with automatic differentiation. ContinuousCloth can be queried at arbitrary timestamps and the same framework supports data-scarce applications, including trajectory interpolation from sparse observations and inverse physical-parameter estimation.
Figure 3: Average of per-rollout runtime across scenarios: RK4 (fixed step size) vs. our ContinuousCloth (CC) method.
MethodS1S2S3S4S5S6
PR ↓\downarrowRMSE ↓\downarrowPR ↓\downarrowRMSE ↓\downarrowPR ↓\downarrowRMSE ↓\downarrowPR ↓\downarrowRMSE ↓\downarrowPR ↓\downarrowRMSE ↓\downarrowPR ↓\downarrowRMSE ↓\downarrow
QRes(w/o MFPSG)4.39×10−34.39\times 10^{-3}7.67×10−17.67\times 10^{-1}4.88×10−34.88\times 10^{-3}5.72×10−15.72\times 10^{-1}8.13×10−28.13\times 10^{-2}4.65×10−14.65\times 10^{-1}9.31×10−29.31\times 10^{-2}3.75×10−13.75\times 10^{-1}4.92×10−24.92\times 10^{-2}7.06×10−17.06\times 10^{-1}4.91×10−24.91\times 10^{-2}7.01×10−17.01\times 10^{-1}
QRes1.17×10−31.17\times 10^{-3}1.24×10−11.24\times 10^{-1}1.73×10−31.73\times 10^{-3}1.01×10−11.01\times 10^{-1}7.98×10−27.98\times 10^{-2}4.66×10−14.66\times 10^{-1}9.17×10−29.17\times 10^{-2}3.76×10−13.76\times 10^{-1}3.93×10−23.93\times 10^{-2}6.44×10−16.44\times 10^{-1}4.11×10−24.11\times 10^{-2}6.67×10−16.67\times 10^{-1}
FLS(w/o MFPSG)4.51×10−34.51\times 10^{-3}7.93×10−17.93\times 10^{-1}4.68×10−34.68\times 10^{-3}5.55×10−15.55\times 10^{-1}4.86×10−34.86\times 10^{-3}3.90×10−13.90\times 10^{-1}4.95×10−34.95\times 10^{-3}2.73×10−12.73\times 10^{-1}5.01×10−35.01\times 10^{-3}4.72×10−14.72\times 10^{-1}5.15×10−35.15\times 10^{-3}5.41×10−15.41\times 10^{-1}
FLS4.37×10−34.37\times 10^{-3}6.68×10−16.68\times 10^{-1}4.53×10−34.53\times 10^{-3}4.39×10−14.39\times 10^{-1}4.77×10−34.77\times 10^{-3}3.64×10−13.64\times 10^{-1}4.87×10−34.87\times 10^{-3}2.55×10−12.55\times 10^{-1}4.76×10−34.76\times 10^{-3}3.84×10−13.84\times 10^{-1}5.92×10−35.92\times 10^{-3}5.34×10−15.34\times 10^{-1}
CC-MLP(w/o MFPSG)2.02×10−32.02\times 10^{-3}1.19×10−11.19\times 10^{-1}1.59×10−31.59\times 10^{-3}1.01×10−11.01\times 10^{-1}2.57×10−32.57\times 10^{-3}9.58×10−29.58\times 10^{-2}3.21×10−33.21\times 10^{-3}1.12×10−11.12\times 10^{-1}2.55×10−22.55\times 10^{-2}8.19×10−18.19\times 10^{-1}2.27×10−22.27\times 10^{-2}7.30×10−17.30\times 10^{-1}
Table 1: Quantitative comparison across S1–S6 scenarios. We report the mean physics residual (PR) in newtons and RMSE in meters over the full rollout horizon for each method. ’w/o MFPSG’ denotes an ablated variant without MFPSG. ’CC’ represents ContinuousCloth.
Figure 4: Qualitative results in the physics-only forward simulation. (a) Trajectory overlay (blue: ground truth, orange: prediction) of ContinuousCloth solver and an RK4 reference [ 39 ] under the same evaluation step size. Three scenarios are S2, S3 and S4. (b) Boundary-mask conditioning enables a single model to handle diverse constraint patterns. (c) Parameter conditioning allows the solver to generalize across different material parameters.
Figure 5: Oscillatory cloth dynamics in the four-corner pinned scenario (S4). Blue shows the high-precision RK4 reference trajectory, and orange shows the ContinuousCloth prediction. The close alignment demonstrates that our model captures the underlying spring–mass oscillations over time.
Figure 6: Qualitative interpolation results across simulation (D2 Moving clean, D3 Swing large-noise) and real data (R1 Shaking clean, R2 Fling outliers). Compared with the MLP baseline, our ContinuousCloth yields more stable and physically plausible trajectories, especially under noisy observations.
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