Better Neural PDE Solvers Through Data-Free Mesh Movers

Authors: Peiyan Hu, Yue Wang, Zhi-Ming Ma

ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git. 6 EXPERIMENTS In the experiments, we evaluate our method on two datasets.
Researcher Affiliation Collaboration Peiyan Hu1, Yue Wang2 , Zhi-Ming Ma1 1Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 2Microsoft Research AI4Science
Pseudocode No The paper does not include any structured pseudocode or algorithm blocks.
Open Source Code Yes The code can be found at: https://github.com/Peiyannn/MM-PDE.git.
Open Datasets No The paper describes methods for generating data (e.g., 'We solve the equation numerically on the uniform 192 × 192 grid with 30 timesteps using a simulation toolkit (Holl et al., 2020)', 'We use FEniCS (Scroggs et al., 2022)... to generate the velocity field'), but does not provide concrete access information (link, DOI, repository, or citation for the dataset itself) for a publicly available dataset used in training.
Dataset Splits No The paper mentions 'training and testing' data but does not explicitly specify a validation dataset split or a methodology for cross-validation.
Hardware Specification Yes Note, the memory of the A100 we use is insufficient when considering parameters of the last two layers simultaneously.
Software Dependencies No The paper mentions 'Pytorch (Paszke et al., 2017)' for automatic gradient computation but does not specify a version number for this or any other software dependency.
Experiment Setup Yes I.1 HYPERPARAMETER SEARCH We conduct experiments for selecting optimal key hyperparameters. The results are presented in Table 12, from which we choose β = 1000, Kitp = 30, Kmp = 35.