ViTO: Vision Transformer-Operator

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named Vision Transformer-Operator (ViTO), combines a U-Net based architecture with a vision transformer. We apply ViTO to solve inverse PDE problems of increasing complexity, including 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 are comparable to or exceed the leading operator network benchmarks for 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 5 times when averaged over the various test cases.