用部分观测数据训练神经微分方程求解器，无需完整数据。
Ambient Physics: Training Neural PDE Solvers with Partial Observations
- 随机掩码已观测数据，让模型无法区分真实缺失与人为遮蔽。
- 相比之前方法，平均误差降低62.51%，函数评估次数减少125倍。
- 只需掩码一个点即可跨架构学习，适合观测受限的科学场景。
在许多科学场景中，获取偏微分方程（PDE）系数和解的完整观测既昂贵又危险甚至不可能。现有基于扩散的方法虽能从部分观测重建场，但需完整观测进行训练。我们提出Ambient Physics框架，直接从部分观测中学习系数-解联合分布，无需任何完整观测。核心思想是随机掩码已观测数据中的子集并进行监督，使模型无法区分“真实未观测”与“人为遮蔽”，从而在全区域生成合理预测。Ambient Physics达到当前最优重建性能：相比先前扩散方法，平均整体误差降低62.51%，同时仅使用125倍更少的函数评估次数。我们还发现“单点过渡”现象：仅掩码一个已观测点，即可实现跨架构与测量模式的学习。该方法为无法获取完整观测的科学领域提供了可行训练路径。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。