Graph Neural PDE Solvers with Conservation and Similarity-Equivariance

Authors: Masanobu Horie, Naoto Mitsume

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

Reproducibility Variable Result LLM Response
Research Type Experimental Our findings from experiments demonstrate that the model s inclusion of physical laws significantly enhances its generalizability, i.e., no significant accuracy degradation for unseen spatial domains while other models degrade.
Researcher Affiliation Collaboration 1RICOS Co. Ltd., Tokyo, Japan 2Graduate School of Science and Technology, University of Tsukuba, Ibaraki, Japan.
Pseudocode No The paper does not contain any pseudocode or clearly labeled algorithm blocks.
Open Source Code Yes The code is available at https://github.com/ yellowshippo/fluxgnn-icml2024.
Open Datasets No For our datasets, we generated 100 trajectories for training, 10 for validation, and 10 for testing. These were derived using the exact solution of the equation, with random variations in uniform velocity u from 0.0 to 0.2, and in the amplitude and phase of the sinusoidal initial condition.
Dataset Splits Yes For our datasets, we generated 100 trajectories for training, 10 for validation, and 10 for testing.
Hardware Specification Yes It was trained on a CPU (Intel Xeon CPU E5-2695 v2 @ 2.40 GHz) for 3 hours... All machine learning models were trained on GPUs (NVIDIA A100 80GB PCIe) over a period of three days.
Software Dependencies Yes We have implemented all our models using Py Torch 1.9.1 (Paszke et al., 2019).
Experiment Setup Yes The model was trained on a CPU (Intel Xeon CPU E5-2695 v2 @ 2.40 GHz) for 3 hours, using MSE loss and an Adam optimizer (Kingma & Ba, 2014)... The hyperparameter employed for the study is detailed in Table 5.