用少量标注数据实现网格模拟的高效超分辨率重建
Semi-Supervised Neural Super-Resolution for Mesh-Based Simulations
- 基于消息传递网络设计互补学习框架，结合少量配对数据与大量未配对数据
- 仅需90%更少的高分辨率数据，误差反而低于全监督基准
- 适合需要降低计算成本的科学模拟场景，尤其适用于数据稀缺领域
基于网格的模拟能高保真求解偏微分方程（PDE），但通常需细密网格，导致计算开销大。超分辨率技术通过从低成本低分辨率（LR）解重建高分辨率（HR）解来缓解此问题。然而，训练神经网络需大量昂贵的HR监督数据。为此，我们提出SuperMeshNet，一种基于消息传递神经网络（MPNN）的高数据效率超分辨率框架。其核心是互补学习：利用少量配对的LR-HR数据和大量未配对的LR数据，通过两个联合训练的互补MPNN模型实现。此外，引入归纳偏置进一步提升性能。实验表明，SuperMeshNet仅需90%更少的HR数据，即可达到比无归纳偏置的全监督基准更低的均方根误差（RMSE）。代码与数据集见https://github.com/jykim-git/SuperMeshNet.git。
原文摘要 · Abstract (English)
Mesh-based simulations provide high-fidelity solutions to partial differential equations (PDEs), but achieving such accuracy typically requires fine meshes, leading to substantial computational overhead. Super-resolution techniques aim to mitigate this cost by reconstructing high-resolution (HR), high-fidelity solutions from low-cost, low-resolution (LR) counterparts. However, training neural networks for super-resolution often demands large amounts of expensive HR supervision data. To address this challenge, we propose SuperMeshNet, an HR data-efficient super-resolution framework for mesh-based simulations aided by message passing neural networks (MPNNs). At its core, SuperMeshNet introduces complementary learning, a semi-supervised approach that effectively leverages both 1) a small amount of paired LR-HR data and 2) abundant unpaired LR data via two jointly trained, complementary MPNN-based models. Additionally, our model is enriched by inductive biases, which are empirically shown to further improve super-resolution performance. Extensive experiments demonstrate that SuperMeshNet requires 90% less HR data to achieve even lower root mean square error (RMSE) than that of the fully supervised benchmark without the inductive biases. The source code and datasets are available at https://github.com/jykim-git/SuperMeshNet.git.
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