Geometric Clifford Algebra Networks
Authors: David Ruhe, Jayesh K Gupta, Steven De Keninck, Max Welling, Johannes Brandstetter
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods. We demonstrate these advantages on a rigid body transformation task, where we simulate the motion of Tetris objects in free space. Next, we show excellent performance on two large-scale PDE modeling tasks of fluid dynamic problems, i.e., weather prediction based on the shallow water equations and fluid systems described by incompressible Navier-Stokes equations. |
| Researcher Affiliation | Collaboration | 1Work done during internship at Microsoft Research. 2Microsoft Autonomous Systems and Robotics Research 3University of Amsterdam 4Microsoft Research AI4Science. Correspondence to: David Ruhe <david.ruhe@gmail.com>, Johannes Brandstetter <johannesb@microsoft.com>. |
| Pseudocode | Yes | Appendix G. Pseudocode |
| Open Source Code | No | The paper provides links to third-party geometric algebra packages (e.g., 'Hadfield et al. (2022) is the go-to package', 'Kahlow (2023b) provides an implementation... in Tensor Flow'), but it does not include an explicit statement or link for the source code of the methodology developed in this paper. |
| Open Datasets | No | The paper describes generating data using modifications of cited simulation packages ('Speedy Weather.jl', 'ΦFlow') or concepts ('Tetris objects' from Thomas et al., 2018), but it does not provide concrete access information (link, DOI, repository) for the specific datasets generated and used in their experiments. |
| Dataset Splits | Yes | We average this loss over 1024 validation and test trajectories. |
| Hardware Specification | Yes | For the Tetris experiments, we used 1 40 GB NVIDIA A100 machines. ... For the fluid dynamics experiments, we used 2 4 16 GB NVIDIA V100 machines. |
| Software Dependencies | No | The paper mentions software like 'Py Torch Geometric', 'Speedy Weather.jl', and 'ΦFlow', and cites their original papers, but does not provide specific version numbers for these software packages or other key dependencies (e.g., 'PyTorch 1.9'). |
| Experiment Setup | Yes | We trained for 2^17 = 131072 steps of gradient descent for all data regimes as reported in the main paper. ... For all models we use the Adam (Kingma & Ba, 2014) optimizer with the default parameter settings (i.e., a learning rate of 10^-3). |