NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data

• URL: http://arxiv.org/abs/2305.18694v2
• Date: Wed, 31 May 2023 06:39:10 GMT
• Title: NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data
• Authors: Songming Liu, Zhongkai Hao, Chengyang Ying, Hang Su, Ze Cheng, Jun Zhu
• Abstract summary: We introduce the Non-Uniform Operator (NUNO) framework for efficient operator learning with non-uniform data. We transform non-uniform data into uniform grids while effectively controlling error, thereby paralleling the speed and accuracy of non-uniform data. Our framework has reduced error rates by up to 60% and enhanced training speeds by 2x to 30x.
• Score: 25.52271761404213
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use mesh-based techniques such as the FFT. To address this, we introduce the Non-Uniform Neural Operator (NUNO), a comprehensive framework designed for efficient operator learning with non-uniform data. Leveraging a K-D tree-based domain decomposition, we transform non-uniform data into uniform grids while effectively controlling interpolation error, thereby paralleling the speed and accuracy of learning from non-uniform data. We conduct extensive experiments on 2D elasticity, (2+1)D channel flow, and a 3D multi-physics heatsink, which, to our knowledge, marks a novel exploration into 3D PDE problems with complex geometries. Our framework has reduced error rates by up to 60% and enhanced training speeds by 2x to 30x. The code is now available at https://github.com/thu-ml/NUNO.

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