CViT: Continuous Vision Transformer for Operator Learning

• URL: http://arxiv.org/abs/2405.13998v2
• Date: Thu, 03 Oct 2024 18:16:07 GMT
• Title: CViT: Continuous Vision Transformer for Operator Learning
• Authors: Sifan Wang, Jacob H Seidman, Shyam Sankaran, Hanwen Wang, George J. Pappas, Paris Perdikaris,
• Abstract summary: Continuous Vision Transformer (CViT) is a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems. CViT combines a vision transformer encoder, a novel grid-based coordinate embedding, and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. We demonstrate CViT's effectiveness across a diverse range of partial differential equation (PDE) systems, including fluid dynamics, climate modeling, and reaction-diffusion processes.
• Score: 24.1795082775376
• License:
• Abstract: Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the Continuous Vision Transformer (CViT), a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems. CViT combines a vision transformer encoder, a novel grid-based coordinate embedding, and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. This design allows for flexible output representations and consistent evaluation at arbitrary resolutions. We demonstrate CViT's effectiveness across a diverse range of partial differential equation (PDE) systems, including fluid dynamics, climate modeling, and reaction-diffusion processes. Our comprehensive experiments show that CViT achieves state-of-the-art performance on multiple benchmarks, often surpassing larger foundation models, even without extensive pretraining and roll-out fine-tuning. Taken together, CViT exhibits robust handling of discontinuous solutions, multi-scale features, and intricate spatio-temporal dynamics. Our contributions can be viewed as a significant step towards adapting advanced computer vision architectures for building more flexible and accurate machine learning models in the physical sciences.

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