FNOPT: Resolution-Agnostic, Self-Supervised Cloth Simulation using Meta-Optimization with Fourier Neural Operators

TL;DR

<3-5 sentence high-level summary> FNOpt tackles the challenge of realistic cloth simulation across multiple mesh resolutions without extensive ground-truth data by coupling a physics-based loss with a resolution-agnostic neural optimizer powered by Fourier Neural Operators. The framework trains a neural optimizer via meta-learning and uses an autoregressive, backward-Euler-inspired update to roll out cloth dynamics, achieving stable, high-fidelity wrinkles across 32×32, 64×64, and 100×100 grids. It significantly improves cross-resolution generalization and boundary-condition robustness compared with state-of-the-art self-supervised and supervised baselines, while maintaining competitive runtimes. The work highlights the potential of neural operators for discretization-invariant physics simulation and introduces a practical, data-efficient path toward reliable cloth simulation across resolutions and boundary configurations.</paper_summary>

Abstract

We present FNOpt, a self-supervised cloth simulation framework that formulates time integration as an optimization problem and trains a resolution-agnostic neural optimizer parameterized by a Fourier neural operator (FNO). Prior neural simulators often rely on extensive ground truth data or sacrifice fine-scale detail, and generalize poorly across resolutions and motion patterns. In contrast, FNOpt learns to simulate physically plausible cloth dynamics and achieves stable and accurate rollouts across diverse mesh resolutions and motion patterns without retraining. Trained only on a coarse grid with physics-based losses, FNOpt generalizes to finer resolutions, capturing fine-scale wrinkles and preserving rollout stability. Extensive evaluations on a benchmark cloth simulation dataset demonstrate that FNOpt outperforms prior learning-based approaches in out-of-distribution settings in both accuracy and robustness. These results position FNO-based meta-optimization as a compelling alternative to previous neural simulators for cloth, thus reducing the need for curated data and improving cross-resolution reliability.

Figures (15)

• Figure 1: Being trained on $32\times32$ mesh, FNOpt generalizes to various mesh resolutions, cloth templates, motion speeds, handle points and trajectories without retraining.
• Figure 2: FNOpt pipeline. At each simulation time step $t$, an inner optimization loop uses an FNO‑based optimizer to predict updates $\Delta \mathbf{a}^{(i)}$ from physics-based loss gradients and state information. After $N$ iterations, backward Euler advances the state to $(\mathbf{x}_t, \mathbf{v}_t)$. Superscript $i$ indicates the inner iteration index.
• Figure 3: Vertex-wise error maps on the xy_v2 sequence on training resolution. Colors indicate the Euclidean distance between rollout and PBS.
• Figure 4: Vertex-wise error maps on finer resolutions on the xy_v2 sequence.
• Figure 5: Per-frame $e_\text{CD}$ ($\times 10^{\!3}$) on xy_v2 sequence. All models are trained at $32\times 32$. FNOpt achieves second lowest error on $32\times32$ resolution and generalizes to the finer $64\times64$ resolution.