Clifford Neural Layers for PDE Modeling
Authors: Johannes Brandstetter, Rianne van den Berg, Max Welling, Jayesh K Gupta
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically evaluate the benefit of Clifford neural layers by replacing convolution and Fourier operations in common neural PDE surrogates by their Clifford counterparts on 2D Navier-Stokes and weather modeling tasks, as well as 3D Maxwell equations. |
| Researcher Affiliation | Industry | Johannes Brandstetter Microsoft Research AI4Science johannesb@microsoft.com Rianne van den Berg Microsoft Research AI4Science rvandenberg@microsoft.com Max Welling Microsoft Research AI4Science maxwelling@microsoft.com Jayesh K. Gupta Microsoft Autonomous Systems and Robotics Research jayesh.gupta@microsoft.com |
| Pseudocode | Yes | We have further include pseudocode for the newly proposed layers in Appendix Section B.6. |
| Open Source Code | Yes | Source code for our Py Torch implementation is available at https://microsoft.github.io/cliffordlayers/ |
| Open Datasets | No | The paper states that data was obtained or generated using tools like ΦFlow and Speedy Weather.jl, but it does not provide concrete access information (specific link, DOI, repository name, formal citation with authors/year, or reference to established benchmark datasets) for the specific datasets generated and used in their experiments. |
| Dataset Splits | No | The paper states, "We evaluate different training set sizes," and provides the number of training trajectories. However, it does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) for training, validation, and test sets. It mentions a "test set" but not its size or how it's separated from the training data. |
| Hardware Specification | Yes | All FNO and CFNO experiments used 4 16 GB NVIDIA V100 machines for training. All Res Net and Clifford Res Net experiments used 8 32 GB NVIDIA V100 machines. |
| Software Dependencies | No | The paper mentions "Py Torch implementation" and tools like "Adam optimizer" and "cosine annealing", as well as data generation tools "ΦFlow" and "Speedy Weather.jl", but it does not provide specific version numbers for these software components to enable replication. |
| Experiment Setup | Yes | We optimized models using the Adam optimizer (Kingma & Ba, 2014) with learning rates [10 4, 2 10 4, 5 10 4] for 50 epochs and minimized the summed mean squared error (SMSE) which is outlined in Equation 79. We used cosine annealing as learning rate scheduler (Loshchilov & Hutter, 2016) with a linear warmup. |