Learning Preconditioners for Conjugate Gradient PDE Solvers
Authors: Yichen Li, Peter Yichen Chen, Tao Du, Wojciech Matusik
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct extensive experiments to demonstrate the efficacy and generalizability of our proposed approach on solving various 2D and 3D linear second-order PDEs. |
| Researcher Affiliation | Academia | 1MIT CSAIL 2Tsinghua University 3Shanghai Qi Zhi Institute. |
| Pseudocode | Yes | Algorithm 1 PCG |
| Open Source Code | No | The paper provides a project webpage link (https://sites.google.com/view/neuralPCG) which is not a direct link to a source-code repository as specified in the guidelines. |
| Open Datasets | No | The dataset is generated by the authors through simulation: 'Our dataset is constructed by simulating trajectories of each PDE on a given mesh domain with various initial conditions and boundary conditions.' No concrete access information (link, DOI, specific citation) for a publicly available dataset was provided. |
| Dataset Splits | No | The paper mentions a 'training set' and 'test set' but does not explicitly describe a separate 'validation' set or its split. |
| Hardware Specification | Yes | All experiments are conducted using the same hardware setup equipped with 64-core AMD CPUs and an NVIDIA RTX-A8000 GPU. |
| Software Dependencies | Yes | All learning-based methods are written using the Pytorch (Paszke et al., 2019) Framework with the Pytorch-Geometric (Fey & Lenssen, 2019) Package and CUDA11.6. |
| Experiment Setup | Yes | We use Adam optimizer with the initial learning rate set to 1e-3. We use a batch size of 16 for all Heat-2d, Poisson-2d, and Wave-2d experimental environments. We use a batch size of 8 for the Poisson-3d environment. Table 6: GNN architecture hyper-parameter. Env Heat-2D Wave-2D Poisson-2D Poisson-3D l 1 1 2 2 h 16 16 16 16 nmp 5 5 5 3 lmp 1 1 2 2 hmp 16 16 16 16 |