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.
@article{arxiv.2303.08891,
title = {ViTO: Vision Transformer-Operator},
author = {Oded Ovadia and Adar Kahana and Panos Stinis and Eli Turkel and George Em Karniadakis},
journal= {arXiv preprint arXiv:2303.08891},
year = {2023}
}