G-Adaptivity: optimised graph-based mesh relocation for finite element methods
Authors: James Rowbottom, Georg Maierhofer, Teo Deveney, Eike Hermann Müller, Alberto Paganini, Katharina Schratz, Pietro Lio, Carola-Bibiane Schönlieb, Chris Budd
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Contributions Our work improves earlier ML based approaches to mesh relocation in the following ways: A novel training mechanism... Thorough numerical comparison with classical and recent approaches in terms of accuracy, mesh quality and computational time. Our experiments include both stationary and time-dependent test cases. Section 5: Experimental results |
| Researcher Affiliation | Academia | 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK 2Department of Computer Science, University of Bath, UK 3Department of Mathematical Sciences, University of Bath, UK 4School of Computing and Mathematical Sciences, University of Leicester, UK 5Laboratoire Jacques-Louis Lions, Sorbonne Universit e, France 6Department of Computer Science and Technology, University of Cambridge, UK. |
| Pseudocode | No | The paper describes the methodology but does not include explicit pseudocode or algorithm blocks. Figure 2 provides a schematic overview of the architecture, and Appendix A.1 describes a process in numbered steps, but these are not formatted as pseudocode. |
| Open Source Code | Yes | Full code to build the datasets and reproduce our results can be found at https://github.com/JRowbottomGit/g-adaptivity. |
| Open Datasets | Yes | Full code to build the datasets and reproduce our results can be found at https://github.com/JRowbottomGit/g-adaptivity. |
| Dataset Splits | Yes | Table 4 shows for each PDE and geometry the number of train and test set samples as will as the resolution or node count for the train, test dataset and evaluation mesh. PDE Poisson Burgers Navier-Stokes Domain Square Polygonal Square Cylinder Train/Test Samples 100/100 100/100 100/100 25/50 Train Resolution [15x15, 20x20] 114 nodes [15x15, 20x20] 201 nodes Test Resolution [12x12,...,23x23] 114 nodes [12x12,...,23x23] 201 nodes Eval Resolution 100x100 228 nodes 100x100 402 nodes |
| Hardware Specification | No | The paper discusses computational efficiency and speed-up but does not provide specific details about the hardware (GPU/CPU models, memory, etc.) used for running experiments. |
| Software Dependencies | Yes | Firedrake (Ham et al., 2023) is a Python framework... dolfin-adjoint (Mitusch et al., 2019) allows the automatic construction of the adjoint problem... The recently added interface to Py Torch (Bouziani & Ham, 2023) is crucial for the work in this paper. The citation for dolfin-adjoint specifically mentions "dolfin-adjoint 2018.1". |
| Experiment Setup | Yes | We train our new model (G-Adapt) and UM2N-G for 300 epochs using an Adam optimiser and learning rate of 0.001. Our model has 4 diffformer blocks as described in Appendix C. Each blocked is rolled out using explicit Euler integration for 32 steps with a step size of 0.1. For the baseline UM2N we trained using 1000 epochs in order to achieve good performance. |