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..
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 | Venue PDF | 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 EMAIL, EMAIL 3 Tsinghua University EMAIL |
| 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. |