Ambient Physics: Training Neural PDE Solvers with Partial Observations

Scientific measurements are often incomplete because observing an entire physical field is expensive, hazardous, or impossible. Existing diffusion-based reconstruction methods can fill in missing regions, but typically still require complete fields during training.

Ambient Physics learns the joint distribution of PDE coefficients and solutions using only partial observations. By masking some measurements that are already available and supervising the model on those hidden values, the method learns to make plausible predictions across the full field without ever seeing a complete training example.

The method achieves state-of-the-art reconstruction performance while using substantially fewer function evaluations than prior diffusion-based approaches, opening a path to neural PDE solvers for scientific settings where complete observations cannot be collected.

Paper: https://arxiv.org/abs/2602.13873