Warm-starting PDE solvers with any-dimensional machine learning

Excerpt

arXiv:2609.38916v1 Announce Type: cross Abstract: Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the GNN transferability literature, we show mathematical conditions under which a partial differential equation (PDE) learning-based solver can be trained in small dimensions and directly applied to solve a higher dimensional PDE in a zero-shot fashion. These conditions are