PhysDEM：稀缺测量下物理定义的时空场生成能量匹配扩散

中文摘要 AI 辅助

从稀缺测量中生成和预测时空物理场具有挑战性，因为观测不足以刻画完整场的分布。这限制了依赖全场数据集的传统数据驱动扩散模型。我们提出PhysDEM，一种物理定义的扩散框架，结合控制方程与空间稀疏观测，生成多个合理场。首先，通过用PDE残差能量重新加权测量条件高斯参考，构建吉布斯目标。其次，推导精确的条件均值恒等式，将去噪简化为对标准化能量诱导均值修正的监督学习。第三，物理位移概率流消除高斯参考项，并通过高斯条件实现变化测量下的摊销采样，无需重新训练。在合成PDE系统和真实世界应用上的实验表明，PhysDEM支持连贯场恢复和高效采样，同时在测试噪声水平下保持稳定诊断，展示其在场评估中的实用价值。据我们所知，PhysDEM是首个无需预组装全场数据集即可实现摊销时空场推断的物理定义扩散模型。

英文摘要

Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a distribution over complete fields. This limits conventional data-driven diffusion models that rely on full-field datasets. We introduce PhysDEM, a physics-defined diffusion framework that combines governing equations with spatially sparse observations to generate multiple plausible fields. First, we construct a Gibbs target by reweighting a measurement-conditioned Gaussian reference with PDE residual energy. Second, we derive an exact conditional-mean identity that reduces denoising to supervised learning of the standardized energy-induced mean correction. Third, a physics-displacement probability flow cancels Gaussian reference terms and enables amortized sampling with changing measurements through Gaussian conditioning, without retraining. Experiments on synthetic PDE systems and real-world-informed applications demonstrate that PhysDEM supports coherent field recovery and efficient sampling while maintaining stable diagnostics under tested noise levels, illustrating its practical value for field assessment. To our knowledge, PhysDEM is the first physics-defined diffusion model enabling amortized spatiotemporal field inference without preassembled full-field datasets.

发表机构

• HKUST（香港科技大学）
• UT Austin（德克萨斯大学奥斯汀分校）

机构由 AI 辅助整理，请以论文原文为准。