MgNO: Efficient Parameterization of Linear Operators via Multigrid
Authors: Juncai He, Xinliang Liu, Jinchao Xu
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our empirical observations reveal that Mg NO exhibits superior ease of training compared to CNNbased models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs). 5 Experiments |
| Researcher Affiliation | Academia | Juncai He , Xinliang Liu & Jinchao Xu King Abdullah University of Science and Technology {juncai.he, xinliang.liu, jinchao.xu}@kaust.edu.sa |
| Pseudocode | Yes | Algorithm 1 u = WMg( f, u1,0; J, νℓ, n) |
| Open Source Code | Yes | The complete code used in our experiments is available at https:// github.com/xlliu2017/Mg NO/. This repository includes all scripts, functions, and necessary files for reproducing our results. |
| Open Datasets | Yes | Datasets employed in our experiments can also be accessed via URLs provided in the repository. The two-phase coefficients and solutions (referred to as Darcy smooth and Darcy rough in Table 5) are generated according to https:// github.com/zongyi-li/fourier_neural_operator/tree/master/data_generation, and used as an operator learning benchmark in (Li et al., 2020; Gupta et al., 2021; Cao, 2021). |
| Dataset Splits | Yes | In the Darcy rough scenario, our data comprises 1280 training, 112 validation, and 112 testing samples. For the Darcy smooth and multiscale trigonometric cases, the split is 1000 training, 100 validation, and 100 testing samples. |
| Hardware Specification | Yes | All experiments were executed on an NVIDIA A100 GPU. |
| Software Dependencies | No | The paper mentions software components like 'Adam optimizer' and 'One Cycle LR scheduler' and refers to 'official implementations' of baselines, but it does not provide specific version numbers for programming languages, libraries (e.g., PyTorch, NumPy), or other software dependencies used in their own implementation. |
| Experiment Setup | Yes | Specifically, optimal models are trained with a batch size of 8, the Adam optimizer, and One Cycle LR with cosine annealing. Although learning rates varied to optimize training across models, Mg NO started with a rate of 5 10 4, decreasing to 2.5 10 6. FNO, UNO, and LSM default to 1 10 3, with a weight decay of 1 10 4. CNN-based models, like UNet and Dil Res Net, have a maximum rate of 5 10 4. All models were trained for 500 epochs. Table 7: Model Configurations |