There is a lot of "neural PDE solvers" with different features and properties. Some work only with regular spatiotemporal grid, some can be applied on arbitrary grids. Some are discrete, some are continuous. Some require a bit of data, some are very data hungry.

So, it depends on what you mean by SOTA.

Fast? FNO or any mapping-based model.

Data-efficient? Some sort of a state space model with GNN-based dynamics and node-wise encoder/decoder.

Time continuity? Something based on neural ODEs dynamics.