In this paper, we present a patch-based representation of surfaces, PolyFit, which is obtained by fitting jet functions locally on surface patches. Such a representation can be learned efficiently in a supervised fashion from both analytic functions and real data. Once learned, it can be generalized to various types of surfaces. Using PolyFit, the surfaces can be efficiently deformed by updating a compact set of jet coefficients rather than optimizing per-vertex degrees of freedom for many downstream tasks in computer vision and graphics. We demonstrate the capabilities of our proposed methodologies with two applications: 1) Shape-from-template (SfT): where the goal is to deform the input 3D template of an object as seen in image/video. Using PolyFit, we adopt test-time optimization that delivers competitive accuracy while being markedly faster than offline physics-based solvers, and outperforms recent physicsguided neural simulators in accuracy at modest additional runtime. 2) Garment draping. We train a self-supervised, mesh- and garment-agnostic model that generalizes across resolutions and garment types, delivering up to an order-ofmagnitude faster inference than strong baselines.

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. Our code is publicly available at https://github.com/Simonhfls/FNOpt.

Recent neural, physics-based modeling of garment deformations allows faster and visually aesthetic results as opposed to the existing methods. Material-specific parameters are used by the formulation to control the garment inextensibility. This delivers unrealistic results with physically implausible stretching. Oftentimes, the draped garment is pushed inside the body which is either corrected by an expensive post-processing, thus adding to further inconsistent stretching; or by deploying a separate training regime for each body type, restricting its scalability. Additionally, the flawed skinning process deployed by existing methods produces incorrect results on loose garments. In this paper, we introduce a geometrical constraint to the existing formulation that is collision-aware and imposes garment inextensibility wherever possible. Thus, we obtain realistic results where draped clothes stretch only while covering bigger body regions. Furthermore, we propose a geometry-aware garment skinning method by defining a body-garment closeness measure which works for all garment types, especially the loose ones. Our code is publicly available at https://github.com/Simonhfls/GAPS.