ViTO: Vision Transformer-Operator
This addresses inverse problems in PDEs like wave and Navier-Stokes equations, offering a more efficient solution for computational physics and engineering applications, though it is incremental as it builds on existing transformer and operator learning methods.
The authors tackled inverse PDE problems by combining vision transformers with operator learning, achieving comparable or better accuracy than leading benchmarks while using less than 10% of the trainable parameters and achieving over 5x speed-up.
We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply ViTO to solve inverse PDE problems of increasing complexity, namely for the wave equation, the Navier-Stokes equations and the Darcy equation. We focus on the more challenging case of super-resolution, where the input dataset for the inverse problem is at a significantly coarser resolution than the output. The results we obtain are comparable or exceed the leading operator network benchmarks in terms of accuracy. Furthermore, ViTO`s architecture has a small number of trainable parameters (less than 10% of the leading competitor), resulting in a performance speed-up of over 5x when averaged over the various test cases.