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NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data
LIU SONGMING · Zhongkai Hao · Chengyang Ying · Hang Su · Ze Cheng · Jun Zhu

Wed Jul 26 02:00 PM -- 03:30 PM (PDT) @ Exhibit Hall 1 #522

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 .

Author Information

LIU SONGMING (Tsinghua University)
Zhongkai Hao (Tsinghua University)
Chengyang Ying (Tsinghua University, Tsinghua University)
Hang Su (Tsinghua University)
Ze Cheng
Jun Zhu (Tsinghua University)

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