Group Equivariant Fourier Neural Operators for Partial Differential Equations
Authors: Jacob Helwig, Xuan Zhang, Cong Fu, Jerry Kurtin, Stephan Wojtowytsch, Shuiwang Ji
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct extensive experiments to evaluate our proposed G-FNO. Results show that explicit encoding of symmetries in FNO architectures leads to consistent performance improvements. We evaluate our models on two commonly used PDEs in the field of computational fluid dynamics: the incompressible Navier-Stokes equations and the shallow water equations. |
| Researcher Affiliation | Academia | 1Department of Computer Science & Engineering, Texas A&M University, TX, USA 2Department of Mathematics, Texas A&M University, TX, USA. Correspondence to: Shuiwang Ji <sji@tamu.edu>. |
| Pseudocode | No | The paper does not contain any sections or figures explicitly labeled 'Pseudocode' or 'Algorithm'. |
| Open Source Code | Yes | Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS). |
| Open Datasets | Yes | For NS-SYM, we generate 1,000 training trajectories, 100 validation trajectories, and 100 test trajectories using the psuedospectral Crank-Nicolson solver from Li et al. (2021a). For NS, we use the data directly from Li et al. (2021a), again with a 1,000/100/100 split. For SWE-SYM, we used numerical data from Takamoto et al. (2022) generated using the finite volume method. For SWE, we follow the methods and splits used by Gupta & Brandstetter (2022) to generate 5,600 training trajectories, 1,120 validation trajectories, and 1,120 test trajectories... |
| Dataset Splits | Yes | For NS-SYM, we generate 1,000 training trajectories, 100 validation trajectories, and 100 test trajectories using the psuedospectral Crank-Nicolson solver from Li et al. (2021a). For NS, we use the data directly from Li et al. (2021a), again with a 1,000/100/100 split. |
| Hardware Specification | Yes | All models are implemented using PyTorch (Paszke et al., 2019) and trained on a single NVIDIA A100 80GB GPU. |
| Software Dependencies | No | The paper mentions 'PyTorch' and 'Adam optimizer' but does not provide specific version numbers for these software components. For instance, it states 'All models are implemented using PyTorch (Paszke et al., 2019)' without a precise version number like 'PyTorch 1.9'. |
| Experiment Setup | Yes | We use 4 Fourier layers for all frequency domain models, truncating the transform to the 12 lowest Fourier modes for all 2D models and 8 spatial/6 temporal Fourier modes for all 3D models... We use the Adam optimizer (Kingma & Ba, 2015) with β1 = 0.9, β2 = 0.999, and weight decay 10^-4. We use batch size of 20 for 2D models and 10 for 3D models with a cosine learning rate scheduler that starts at 10^-3 and is decayed to 0. 3D models are trained for 500 epochs or until the validation loss does not improve for 100 successive epochs, while 2D models are trained for 100 epochs. |