具有稀疏监督的不确定性校准时空场扩散
Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision
AI总结：
SOLID通过稀疏监督学习时空动态，实现高精度不确定性校准的场重建。
摘要：
物理场通常只在稀疏且随时间变化的传感器位置被观测到，这使得预测和重建变得不成立且不确定性至关重要。我们提出了SOLID，一种基于掩码的扩散框架，该框架仅从稀疏观测中学习时空动态：训练和评估仅使用观测到的目标位置，不需要密集场和预插值。与以往工作不同，SOLID仅使用稀疏监督进行端到端训练。SOLID在去噪步骤中将测量值及其位置作为条件，并引入了双掩码目标，即（i）强调学习在未观测的空地区域的同时，（ii）增加输入和目标提供最可靠锚点的重叠像素的权重。这种严格的稀疏条件路径使后验采样出与测量一致的完整场，从而在概率误差方面提高了一个数量级，即使在极端稀疏情况下也能生成校准的不确定性地图（ρ>0.7）。
英文摘要：
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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