用概率模型实现物理模拟超分辨率，无需大量标注数据且自带不确定性评估。
Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification
- 结合统计有限元与能量生成模型，实现无监督超分辨率建模。
- 在2D泊松方程上实现计算速度提升，同时输出可靠不确定性估计。
- 适合需要快速高保真模拟与风险评估的工程场景。
超分辨率（SR）是通过低分辨率数据生成物理系统高保真模拟的有力工具，可在工程应用中实现快速准确预测。然而，现有基于深度学习的SR方法依赖大规模标注数据集，且缺乏可靠的不确定性量化（UQ），限制了其在真实场景中的应用。为此，我们提出一种概率性超分辨率框架，融合统计有限元法与基于能量的生成建模。该方法在无需大量标注数据的情况下，实现高效的高分辨率预测并内嵌不确定性量化。在二维泊松问题上的验证表明，该方法相较高分辨率数值求解器具有显著计算加速，同时提供可靠的不确定性估计。
原文摘要 · Abstract (English)
Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR methods, require large labeled datasets and lack reliable uncertainty quantification (UQ), limiting their applicability in real-world scenarios. To overcome these challenges, we propose a probabilistic SR framework that leverages the Statistical Finite Element Method and energy-based generative modeling. Our method enables efficient high-resolution predictions with inherent UQ, while eliminating the need for extensive labeled datasets. The method is validated on a 2D Poisson example and compared with bicubic interpolation upscaling. Results demonstrate a computational speed-up over high-resolution numerical solvers while providing reliable uncertainty estimates.
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