In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require complete observations for training. We introduce Ambient Physics, a framework for learning the joint distribution of coefficient-solution pairs directly from partial observations, without requiring a single complete observation. The key idea is to randomly mask a subset of already-observed measurements and supervise on them, so the model cannot distinguish "truly unobserved" from "artificially unobserved", and must produce plausible predictions everywhere. Ambient Physics achieves state-of-the-art reconstruction performance. Compared with prior diffusion-based methods, it achieves a 62.51$\%$ reduction in average overall error while using 125$\times$ fewer function evaluations. We also identify a "one-point transition": masking a single already-observed point enables learning from partial observations across architectures and measurement patterns. Ambient Physics thus enables scientific progress in settings where complete observations are unavailable.

翻译：在许多科学场景中，获取偏微分方程系数与解的完整观测数据往往成本高昂、存在风险甚至无法实现。现有基于扩散的方法能够根据部分观测重建物理场，但其训练过程仍需完整观测数据。本文提出环境物理框架，该框架能够直接从部分观测数据中学习系数-解对的联合分布，且无需任何完整观测样本。其核心思想是：对已观测测量值的随机子集进行掩码处理并以此监督模型训练，使得模型无法区分"真实未观测"与"人工未观测"区域，从而必须在全域生成合理的预测。环境物理框架实现了当前最优的重建性能：相较于先前的扩散方法，在平均整体误差降低62.51%的同时，函数评估次数减少125倍。我们还发现了"单点跃迁"现象：仅需掩码单个已观测点，即可实现跨架构与测量模式的部分观测学习。因此，环境物理框架为在无法获得完整观测数据的场景中推动科学研究提供了新的可能。