用可解释的偏微分方程表示法，实现稀疏观测下的高保真重建与超分辨。
Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity
- 将潜在变量直接设为控制PDE的系数与源项，构建可解释潜空间。
- 在多种结构化数据缺失场景下实现高保真动态重建与不确定性追踪。
- 适合需要物理可解释性的科学计算、气候模拟等领域的研究者。
科学测量常受限于噪声、空间覆盖不全或分辨率不足，导致场重建困难。我们提出LatentPDE，一种潜在扩散框架，可同时解决稀疏观测重建与超分辨率问题。现有物理引导的扩散模型通常依赖软损失惩罚或不可解释表示，而本方法通过构造内在可解释的潜在空间实现物理一致性：将潜在变量直接参数化为假设控制方程的系数与源项。该设计使模型能在高度差异且结构化的数据缺失条件下可靠重构动态。在多种配置下的实证结果表明，模型可在任意期望分辨率下实现高保真恢复，并准确追踪底层预测不确定性。
原文摘要 · Abstract (English)
Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent diffusion framework designed to simultaneously resolve sparse-observation reconstruction and super-resolution. While existing physics-guided diffusion models typically rely on soft loss penalties or uninterpretable representations, our approach enforces physical compliance by constructing an inherently interpretable latent space. Specifically, we parameterize the latent variables directly as the coefficients and source terms of an assumed governing PDE. In doing so, LatentPDE is able to reliably reconstruct dynamics across highly disparate and structured data gaps. Empirical results on diverse configurations demonstrate that our model achieves high-fidelity recovery at any desired resolution while also tracking the underlying predictive uncertainty.
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