发表机构
The Hong Kong University of Science and Technology; University of Michigan; HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute（香港科技大学; 密歇根大学; 香港科技大学深圳-香港协同创新研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对PDE逆问题的不适定性，提出OCL-PDE生成框架，利用观测互补潜变量结合观测重建未知场，基于物理感知AE和条件流匹配，提升重建精度与细节恢复。
AI 中文摘要
偏微分方程（PDE）逆问题通常是不适定的，使得精细尺度细节难以恢复。我们通过引入一种学习得到的观测互补潜变量表示来解决这一问题，该表示保留与重建相关的信息，并与观测相结合以重建未知场。基于这一表示，我们提出了OCL-PDE，一种生成框架，鼓励观测引导大尺度结构，而潜变量提供互补的精细尺度细节。OCL-PDE基于物理感知自编码器（AE）和条件流匹配构建，支持逆重建以及正向PDE预测。实验表明，与评估的基线相比，重建精度和精细细节恢复均有所提高。
英文摘要
Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.
