AI 中文总结
本文通过公平比较确定性U-Net、条件扩散和先验引导扩散在多个物理场重建任务中的表现，发现扩散模型并非普遍优于确定性回归，其优势取决于场特性和观测稀疏度，并明确了不同方法在准确性、不确定性估计和稳健性上的适用条件。
AI 中文摘要
从稀疏观测重建物理场是系统辨识、预测和控制的核心问题，然而稀疏测量通常无法唯一确定完整场。这使得重建成为一个不适定的逆问题，而非简单的插值。尽管已经开发了许多确定性和生成性方法，但对于何时单个点估计足够、何时一组合理重建的分布更有用，仍缺乏明确共识。我们在匹配的实验设置下对确定性U-Net、条件扩散和先验引导扩散进行了公平比较，包括二维泊松方程、二维纳维-斯托克斯流动和一维Kuramoto-Sivashinsky动力学。通过这一比较，我们得出三点观察。第一，准确性依赖于场和状态区域，扩散在更高复杂度或更稀疏观测下并无系统性优势。第二，集成均值提高了相位对齐的准确性，而单个样本能更好地保持变异性，并在选定状态区域中保留高波数能量。第三，条件扩散以较低成本提供更可靠的不确定性估计，而先验引导扩散对掩码分布偏移更稳健，但需要显著更高的推理成本和引导调优。这些结果阐明了生成性重建何时有用，并为改进稀疏场重建中的不确定性估计、细尺度样本保真度、稳健性和计算效率提供了指导。
英文摘要
Reconstructing physical fields from sparse observations is central to system identification, forecasting, and control, yet sparse measurements generally underdetermine the full field. This makes reconstruction an ill-posed inverse problem rather than simple interpolation. Although many deterministic and generative methods have been developed, there is still no clear consensus on when a single point estimate is sufficient and when a distribution of plausible reconstructions is more useful. We conduct a fair comparison of a deterministic U-Net, conditional diffusion, and prior-guided diffusion under matched experimental settings, including 2D Poisson equation, 2D Navier-Stokes flow, and 1D Kuramoto-Sivashinsky dynamics. Through this comparison, we make three observations. First, accuracy is field- and regime-dependent, with no systematic advantage for diffusion under higher complexity or sparser observations. Second, ensemble means improve phase-aligned accuracy, whereas individual samples better preserve variability and can retain high-wavenumber power in selected regimes. Third, conditional diffusion provides more reliable uncertainty estimates at lower cost, while prior-guided diffusion is more robust to mask-distribution shifts but requires substantially higher inference cost and guidance tuning. These results clarify when generative reconstruction is useful and provide guidance for improving uncertainty estimation, fine-scale sample fidelity, robustness, and computational efficiency in sparse field reconstruction.
Comments33 pages, 15 figures, including appendices
