Accelerating Data Generation for Neural Operators via Krylov Subspace Recycling
Authors: Hong Wang, Zhongkai Hao, Jie Wang, Zijie Geng, Zhen Wang, Bin Li, Feng Wu
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Both theoretical analysis and extensive experiments demonstrate that SKR can significantly accelerate neural operator data generation, achieving a remarkable speedup of up to 13.9 times. |
| Researcher Affiliation | Academia | Hong Wang1,2 , Zhongkai Hao3 , Jie Wang1,2 , Zijie Geng1,2, Zhen Wang1,2, Bin Li1,2, Feng Wu1,2 1 CAS Key Laboratory of Technology in GIPAS, University of Science and Technology of China 2 Mo E Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China {wanghong1700,ustcgzj,wangzhen0518}@mail.ustc.edu.cn, {jiewangx,binli,fengwu}@ustc.edu.cn 3 Tsinghua University hzj21@mails.tsinghua.edu.cn |
| Pseudocode | Yes | Algorithm 1: The Sorting Algorithm; Algorithm 2: GCRO-DR |
| Open Source Code | Yes | Codes are available at https://github.com/wanghong1700/NO-Data Gen-SKR. |
| Open Datasets | Yes | To probe the algorithm s adaptability across matrix types, we delved into four distinct linear equation challenges, each rooted in a PDE: 1. Darcy Flow Problem (Li et al., 2020; Rahman et al., 2022; Kovachki et al., 2021; Lu et al., 2022); 2. Thermal Problem (Sharma et al., 2018; Koric & Abueidda, 2023); 3. Poisson Equation (Hsieh et al., 2019; Zhang et al., 2022); 4. Helmholtz Equation (Zhang et al., 2022). |
| Dataset Splits | No | The paper states '5000 were designated for the training set and 256 for the test set' in Appendix E.3.2, but no explicit validation split is provided. |
| Hardware Specification | Yes | 1. Environment (Env1): Platform: Docker version 20.10.0 Operating System: Ubuntu 22.04.3 LTS Processor: Dual-socket Intel Xeon Gold 6154 CPU, clocked at 3.00GHz 2. Environment (Env2): Platform: Windows 11, version 21H2, WSL Operating System: Ubuntu 22.04.3 LTS Processor: 13th Gen Intel Core i7-13700KF, clocked at 3.40 GHz |
| Software Dependencies | Yes | We utilized the latest version from PETSc 3.19.4 for GMRES. |
| Experiment Setup | Yes | Our analysis centered on two primary performance metrics viewed through three perspectives. These tests spanned four different datasets, with SKR consistently delivering commendable results. Specifically, the three Perspectives are: 1. Matrix preconditioning techniques, spanning 7 to 10 standard methods. 2. Accuracy criteria for linear system solutions, emphasizing 5 to 8 distinct tolerances. 3. Different matrix sizes, considering 5 to 6 variations. Our primary performance Metrics encompassed: 1. Average computational time overhead. 2. Mean iteration count. |