GIT-Net: Generalized Integral Transform for Operator Learning
Authors: Chao Wang, Alexandre H. Thiery
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments demonstrate that GIT-Net is a competitive neural network operator, exhibiting small test errors and low evaluations across a range of PDE problems. This stands in contrast to existing neural network operators, which typically excel in just one of these areas. |
| Researcher Affiliation | Academia | Chao Wang EMAIL Department of Statistics and Data Science National University of Singapore Alexandre Hoang Thiery EMAIL Department of Statistics and Data Science National University of Singapore |
| Pseudocode | No | The paper describes procedures and architectures using prose and diagrams (e.g., Section 2.1 describes the GIT mapping in numbered steps, and Figure 1 illustrates it), but it does not contain a formally labeled pseudocode or algorithm block with structured steps. |
| Open Source Code | Yes | Codes and datasets are publicly available 1. 1Github: https://github.com/chaow-mat/General_Integral_Transform_Neural_Network |
| Open Datasets | Yes | Codes and datasets are publicly available 1. 1Github: https://github.com/chaow-mat/General_Integral_Transform_Neural_Network |
| Dataset Splits | Yes | To evaluate the performance of the different methods, four training datasets of respective size Ntrain {2500, 5000, 10000, 20000} were generated for training; the methods were evaluated on independent test sets. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU models, CPU types, or memory specifications used for running the experiments. It discusses computational costs but not the hardware on which these computations were performed. |
| Software Dependencies | No | The paper mentions the ADAM optimizer (Kingma & Ba, 2015) and GELU nonlinearity (Hendrycks & Gimpel, 2016), as well as automatic differentiation frameworks (Bradbury et al., 2018; Paszke et al., 2017) which refer to JAX and PyTorch, but it does not specify version numbers for any of these software components. |
| Experiment Setup | Yes | The numerical experiments presented in Section 5, we used the ADAM optimizer (Kingma & Ba, 2015). The number L 1 of GIT layers is fixed at L = 3 and we used C {2, 4, 8, 16, 32} and K {16, 64, 128, 256, 512}. The GELU nonlinear activation function (Hendrycks & Gimpel, 2016) was used to implement the GIT-Net. Following the setup of the Fourier Neural Operator (FNO) in de Hoop et al. (2022), we used twelve Fourier modes and three Fourier Neural Layers (L = 3 in (20)). For the PCA-Net, as in de Hoop et al. (2022), we use four internal layers (4-layer MLP in (17)). |