Principled Acceleration of Iterative Numerical Methods Using Machine Learning
Authors: Sohei Arisaka, Qianxiao Li
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the significant advantage and versatility of the proposed approach through various numerical applications. In Section 4, we demonstrate the significant performance improvement and versatility of the proposed method through numerical examples, including nonlinear differential equations and nonstationary iterative methods. |
| Researcher Affiliation | Collaboration | 1Department of Mathematics, National University of Singapore 2Kajima Corporation, Japan. |
| Pseudocode | Yes | Algorithm 1 GBMS for minimizing the number of iterations |
| Open Source Code | No | The paper does not contain any statement about making its own code open-source or providing a link to a code repository. |
| Open Datasets | No | The paper describes how data is generated/sampled for the experiments (e.g., "sample c1, c2, c3 log-uniformly from [10-4, 1], [105, 109], [102, 106] respectively" and "We sampled tasks 1,000 for training, 1,000 for validation, and 1,000 for test"). This indicates data generation and use, not concrete access to a pre-existing public dataset. |
| Dataset Splits | Yes | The number of tasks for training, validation, and test are all 10^3. We prepare 10,000 sets of c1, c2, c3 and use 2,500 for training, 2,500 for validation, and 5,000 for test. We sampled tasks 1,000 for training, 1,000 for validation, and 1,000 for test. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments (e.g., GPU model, CPU type, memory). |
| Software Dependencies | No | The paper mentions software like FEniCS and SciPy but does not provide specific version numbers for these or other key software components used in their implementation that would be necessary for reproduction. |
| Experiment Setup | Yes | Network architecture and hyper-parameters In Section 2.2.1 and Section 3.1.2, Ψnn is a fully connected neural network with two hidden layers of 15 neurons. The optimizer is Adam (Kingma & Ba, 2015) with learning rate 0.01 and (β1, β2) = (0.999, 0.999). The batch size is 256. The model is trained for 2500 epochs. Network architecture and hyper-parameters In Section 4.1, Ψini, Ψrelax, and Ψboth are fully-connected neural networks that take c1, c2, c3, hn, yn as an input. They have two hidden layers with 1024 neurons. The meta-solvers are trained for 200 epochs by Adam with batchsize 16384. The initial learning rate is 2.0 × 10−5. |