Ambient Physics: Training Neural PDE Solvers with Partial Observations

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.

Solaris: A Foundation Model of the Sun

Foundation models have demonstrated remarkable success across various scientific domains, motivating our exploration of their potential in solar physics. In this paper, we present Solaris, the first foundation model for forecasting the Sun's atmosphere. We leverage 13 years of full-disk, multi-wavelength solar imagery from the Solar Dynamics Observatory, spanning a complete solar cycle, to pre-train Solaris for 12-hour interval forecasting. Solaris is built on a large-scale 3D Swin Transformer architecture with 109 million parameters. We demonstrate Solaris' ability to generalize by fine-tuning on a low-data regime using a single wavelength (1700 {\AA}), that was not included in pre-training, outperforming models trained from scratch on this specific wavelength. Our results indicate that Solaris can effectively capture the complex dynamics of the solar atmosphere and transform solar forecasting.