Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Learning Preconditioners for Conjugate Gradient PDE Solvers
Authors: Yichen Li, Peter Yichen Chen, Tao Du, Wojciech Matusik
ICML 2023 | Venue PDF | 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 |