仅用稀疏观测数据，实现物理场的高精度概率预测与可信不确定性估计。
Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision
- 基于掩码条件扩散模型，直接从稀疏观测学习时空动态。
- 在严重稀疏条件下，概率误差降低一个数量级，不确定性校准率超0.7。
- 适合气象、海洋等传感器稀疏场景下的预测与风险评估。
物理场通常仅在稀疏且随时间变化的传感器位置被观测，导致预测与重建问题病态且不确定性关键。我们提出SOLID，一种掩码条件扩散框架，仅依靠稀疏观测即可学习时空动态：训练与评估均仅使用观测目标位置，无需密集场数据或预插值。与以往在密集再分析或模拟数据上训练、仅在稀疏条件下测试的工作不同，SOLID全程仅以稀疏监督进行端到端训练。SOLID在每一步去噪过程中同时依赖测量值及其位置，并引入双重掩码目标：(i) 强化未观测区域的学习，(ii) 提升输入与目标重叠像素的权重，使其成为最可靠的锚点。这种严格的稀疏条件路径，使后验采样生成的完整场与观测一致，在严重稀疏条件下，概率误差最高提升一个数量级，不确定性校准率ρ > 0.7。
原文摘要 · Abstract (English)
Physical fields are typically observed only at sparse, time-varying sensor locations, making forecasting and reconstruction ill-posed and uncertainty-critical. We present SOLID, a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone: training and evaluation use only observed target locations, requiring no dense fields and no pre-imputation. Unlike prior work that trains on dense reanalysis or simulations and only tests under sparsity, SOLID is trained end-to-end with sparse supervision only. SOLID conditions each denoising step on the measured values and their locations, and introduces a dual-masking objective that (i) emphasizes learning in unobserved void regions while (ii) upweights overlap pixels where inputs and targets provide the most reliable anchors. This strict sparse-conditioning pathway enables posterior sampling of full fields consistent with the measurements, achieving up to an order-of-magnitude improvement in probabilistic error and yielding calibrated uncertainty maps (\r{ho} > 0.7) under severe sparsity.
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