Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
International Conference on Machine Learning (ICML), 2026
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many critical applications remain constrained by the substantial computational costs …
Ambient Physics: Training Neural PDE Solvers with Partial Observations
In many scientific contexts, obtaining complete observations of PDE coefficients and solutions proves expensive, hazardous, or unfeasible. Recent diffusion-based approaches can reconstruct fields from incomplete data, yet require fully observed examples during training. We present Ambient Physics, a framework enabling …