Neural Krylov Iteration for Accelerating Linear System Solving
Authors: Jian Luo, Jie Wang, Hong Wang, huanshuo dong, Zijie Geng, Hanzhu Chen, Yufei Kuang
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide extensive experiments and comprehensive theoretical analyses to demonstrate the feasibility and efficiency of Neur KItt. In our main experiments, Neur KItt accelerates the solving of linear systems across various settings and datasets, achieving up to a 5.5 speedup in computation time and a 16.1 speedup in the number of iterations. |
| Researcher Affiliation | Academia | 1Mo E Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China {jianluo,wanghong1700}@mail.ustc.edu.cn jiewangx@ustc.edu.cn |
| Pseudocode | Yes | A Algorithmic Details A.2 Neur KItt Pseudocode Algorithm 1: Neur KItt Krylov subspace iteration |
| Open Source Code | Yes | Our code is available at https://github.com/smart-JLuo/Neur KItt |
| Open Datasets | Yes | Datasets. To investigate the algorithm s adaptability to various types of matrices, we examined three different linear equation challenges, each rooted in a PDE: 1. Helmholtz Equation [62]. 2. Darcy Flow Problem [31, 44, 27, 36]; 3. Non-uniform Heat Conduction Equation [48, 25, 4, 18]. |
| Dataset Splits | No | For darcy flow and heat datasets, we generate 8000 samples for training and 1600 samples for testing. For Helmholtz, we generate 1000 samples for training and 200 samples for testing. The paper specifies training and testing sample counts but does not explicitly mention a separate validation split or its size. |
| Hardware Specification | Yes | F.2 Environment To ensure consistency in our evaluations, all comparative experiments were conducted under uniform computing environments. Specifically, the environments used are detailed as follows: CPU: Intel Xeon Gold 6246R CPU @ 3.40GHz GPU: NVIDIA Ge Force RTX 3090 |
| Software Dependencies | Yes | For the GMRES solver, we employed the most recent version of PETSc, specifically 3.19.4. |
| Experiment Setup | Yes | Model Training and Predicting: We employ the 5 FNO layers with modes from {20, 32, 40} and the width from {32, 50, 64}. The learning rate is fix at 1 10 3 while the batch size is selected from {16, 32}. The number of subspace dimensions is fixed at 10 in all experiments. |