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[2602.13873] Ambient Physics: Training Neural PDE Solvers with Partial Observations
Summary
The paper introduces 'Ambient Physics', a novel framework for training neural PDE solvers using partial observations, achieving significant improvements in reconstruction performance without requiring complete data.
Why It Matters
This research addresses the challenge of incomplete data in scientific modeling, which is often costly or impractical to obtain. By enabling effective learning from partial observations, it opens new avenues for scientific progress in various fields where full data acquisition is not feasible.
Key Takeaways
- Ambient Physics allows training of neural PDE solvers with only partial observations.
- The framework reduces average overall error by 62.51% compared to previous methods.
- It requires 125 times fewer function evaluations, enhancing efficiency.
- The 'one-point transition' concept enables learning across different architectures.
- This approach is crucial for scientific applications where complete data is unattainable.
Computer Science > Artificial Intelligence arXiv:2602.13873 (cs) [Submitted on 14 Feb 2026] Title:Ambient Physics: Training Neural PDE Solvers with Partial Observations Authors:Harris Abdul Majid, Giannis Daras, Francesco Tudisco, Steven McDonagh View a PDF of the paper titled Ambient Physics: Training Neural PDE Solvers with Partial Observations, by Harris Abdul Majid and 3 other authors View PDF HTML (experimental) Abstract: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 ...
