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ViTO: Vision Transformer-Operator
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DOI：10.1016/j.cma.2024.117109.png)
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Abstract
En 中文
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.
Keywords:
Deep learning
Vision Transformers
Scientific machine learning
Inverse problems
Super-resolution
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