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arXiv · 2303.08891

ViTO: Vision Transformer-Operator

Oded Ovadia·Adar Kahana·Panos Stinis·Eli Turkel·George Em Karniadakis
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Abstract

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.

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Oded Ovadia, Adar Kahana, Panos Stinis, Eli Turkel, George Em Karniadakis. 2023-03-15. ViTO: Vision Transformer-Operator. https://arxiv.org/abs/2303.08891

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