Wavelet Diffusion Neural Operator
Authors: Peiyan Hu, Rui Wang, Xiang Zheng, Tao Zhang, Haodong Feng, Ruiqi Feng, Long Wei, Yue Wang, Zhi-Ming Ma, Tailin Wu
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D highdimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-Westlake U/wdno.git. |
| Researcher Affiliation | Collaboration | 1Department of Artificial Intelligence, School of Engineering, Westlake University, 2Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 3Fudan University, 4South China University of Technology, 5Microsoft AI4Science |
| Pseudocode | Yes | To help understand the entire algorithm, we provide the pseudocode of WDNO s training and inference in Algorithm 1, and the visualization of WDNO s entire training and inference on 1D Burgers equation in Figure 10. |
| Open Source Code | Yes | The code can be found at https://github.com/AI4Science-Westlake U/wdno.git. |
| Open Datasets | Yes | We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. ... The ERA5 dataset (Kalnay et al., 2018), provided by ECMWF, is a challenging real-world dataset for weather forecasting. ... We consider a particularly challenging scenario from the 1D CFD dataset in PDEBench (Takamoto et al., 2022). |
| Dataset Splits | Yes | For the Burgers equation control task, we generate another 50 trajectories for testing. For the super-resolution task, we generate another 2000 trajectories for testing in the 0 super-resolution task (which is the original resolution). In 1, 2, 3 super-resolution tasks, another 100 samples are generated and shared across the three different super-resolution settings. |
| Hardware Specification | Yes | Both times are recorded on an A100 GPU with a batch size of 2000. ... We provide inference times for a batch size of 1 on A100 in Table 11. ... 1D train (A100) ... 2D train (2A100) |
| Software Dependencies | Yes | We perform a 2D wavelet transform on the original data using the bior2.4 wavelet basis and the periodization mode, implemented using the pytorch_wavelets package (Cotter, 2019). ... We performed a 3D wavelet transform on the original data using the bior1.3 wavelet basis and zero mode, implemented through the Pytorch Wavelet Toolbox (ptwt) (Wolter et al., 2024). |
| Experiment Setup | Yes | The hyperparameters on WDNO are recorded in Table 18. ... The hyperparameters of the 3D-Unet architecture are in the Table 20. ... The detailed values of hyperparameters are provided in Table 22. ... The specific hyperparameters utilized are detailed in Table 25. |