Semi-Supervised Neural Super-Resolution for Mesh-Based Simulations

Mesh subdivision is a fundamental operation for converting coarse, editable meshes into high-resolution surfaces, with broad applications in digital asset creation. Classical rule-based schemes rely on fixed local refinement rules and often produce over-smoothed surfaces. Recent neural subdivision methods improve detail synthesis, but remain constrained by local modeling and exhibit limited generalizability. We present SubdivAR, a neural mesh subdivision framework based on our proposed Mesh Autoregressive Representation (MAR). MAR arranges meshes at different subdivision levels into an ordered scale sequence, reformulating subdivision as autoregressive next-scale prediction. To support this formulation, we introduce a Hybrid Topology-Aware Transformer that combines global semantic attention with topology-constrained local feature aggregation. SubdivAR adopts a next-scale coordinate prediction paradigm, regressing vertex offsets at each refinement stage to preserve subdivision topology while recovering fine-grained geometric details. To enable reliable learning, we construct FII-40K, a curated dataset of nearly 40,000 high-quality meshes with multi-level subdivision supervision. Experiments show that SubdivAR outperforms state-of-the-art baselines, reducing Hausdorff Distance and Chamfer Distance by 18.8% and 14.2%, respectively, and demonstrates strong robustness on complex open-surface geometries.

Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both classical numerical solvers and existing neural approaches. While neural methods have shown promising results under moderately sparse observations, their inference efficiency at high resolutions is limited, and their accuracy degrades substantially in the extremely sparse regime. In this work, we propose the Di-BiLPS, a unified neural framework that effectively handle both forward and inverse PDE problems under extremely sparse observations. Di-BiLPS combines a variational autoencoder to compress high-dimensional inputs into a compact latent space, a latent diffusion module to model uncertainty, and contrastive learning to align representations. Operating entirely in this latent space, the framework achieves efficient inference while retaining flexible input-output mapping. In addition, we introduce a PDE-informed denoising algorithm based on a variance-preserving diffusion process, which further improves inference efficiency. Extensive experiments on multiple PDE benchmarks demonstrate that Di-BiLPS consistently achieves SOTA performance under extremely sparse inputs (as low as 3%), while substantially reducing computational cost. Moreover, Di-BiLPS enables zero-shot super-resolution, as it allows predictions over continuous spatial-temporal domains.

Linear recurrent unit (LRU), designed with a principled formulation for stable linear recurrence, has demonstrated promising accuracy and robustness on long-range dependency tasks. However, its static parameterization and single-scan method limits its applicability to 2D vision tasks. In this study, we propose a LRU-based restoration network with a semantic modulating unit (SMU) to achieve a harmonious balance between performance and efficiency in single-image super-resolution. The SMU plays three key roles: LRU modulation, spatial categorization, and feature enhancement through learned prototype. Extensive experiments demonstrate that our method quantitatively and qualitatively surpasses recent state-of-the-art methods. Notably, our approach achieves superior performance with computational complexity on par with existing methods. The source code and models are available at https://github.com/MingyuChoi-run/LSM