General Covariance Data Augmentation for Neural PDE Solvers
Authors: Vladimir Fanaskov, Tianchi Yu, Alexander Rudikov, Ivan Oseledets
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To evaluate the efficiency of our approach, we perform empirical tests on the two-way wave, convection-diffusion, and stationary diffusion equations using several variants of Fourier Neural Operator (FNO) (Li et al., 2020), Deep Operator Network (Deep ONet) (Lu et al., 2021a), Multilayer Perceptron (MLP) (Haykin, 1994), Dilated Residual Network (Dil Res Net) (Yu & Koltun, 2015), (Stachenfeld et al., 2021) and U-Net (Ronneberger et al., 2015). Both for one-dimensional and two-dimensional PDEs proposed augmentation technique improves test error by 23% on average and up to 80% in the most favorable cases. |
| Researcher Affiliation | Academia | 1Skoltech, Center for Artificial Intelligence Technology 2Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences 3Artificial Intelligence Research Institute. |
| Pseudocode | No | The paper describes procedures and transformations with mathematical equations and descriptive text but does not include any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Code and datasets are available on https://github. com/VLSF/augmentation. |
| Open Datasets | Yes | Code and datasets are available on https://github. com/VLSF/augmentation. Links to the datasets are available in the repository https://github.com/VLSF/ augmentation. Datasets can be downloaded from https://disk.yandex.ru/d/Ar C6j T3TZc Kncw. |
| Dataset Splits | No | The paper mentions 'Ntrain' and 'Ntest' for dataset sizes and uses them for evaluation in tables, but there is no explicit mention of a separate 'validation' split or how it's handled (e.g., specific percentages or counts for training/validation/test splits). For D=1 problems, it mentions 'Ntrain = 500, 1000, 1500, 2000; Ntest = 1000' in Section 4.3, but no validation split is described. |
| Hardware Specification | No | The paper describes neural network architectures and training parameters (learning rate, batch size, epochs) but does not provide specific details on the hardware used, such as GPU models, CPU types, or memory. |
| Software Dependencies | No | The paper mentions neural network frameworks like 'Deep ONet (Lu et al., 2021a) and FNO (Li et al., 2020), implemented in https://github.com/lu-group/deeponet-fno and https://github.com/neural-operator/ fourier_neural_operator, respectively.' However, it does not provide specific version numbers for these libraries or other software dependencies like Python, PyTorch, or TensorFlow. |
| Experiment Setup | Yes | Appendix C. Architectures and training details: In this section, we provide extended comments on the architectures used and collect in Table 5 the description of the optimization process. Table 5. Training details: ν learning rate, ν decay / epoch weight decay per epoch, Nepoch number of epoch used for training, Nbatch batch size, Nparams number of network parameters. For example, for FNO, learning rate is 10^-3, weight decay 10^-4, 500 epochs, 200 batch size for D=1, etc. Detailed descriptions of neural networks like FNO, Deep ONet, MLP, Dil Res Net, U-Net, and SNO, including their number of layers, features, modes, and activation functions, are also provided within Appendix C. |