This paper proposes an effective data generation-based operator learning method to solve partial differential equations (PDEs), including nonlinear cases, defined on unbounded domains.
A novel distributed training approach enables a single neural operator with significantly fewer parameters to effectively tackle multi-operator learning challenges, without incurring additional average costs.
The author introduces DPOT, a novel auto-regressive denoising pre-training strategy based on Fourier attention for large-scale PDE pre-training. This approach aims to enhance performance on downstream tasks by leveraging diverse PDE datasets.