An Interpretable Approach to the Solutions of High-Dimensional Partial Differential Equations
Authors: Lulu Cao, Yufei Liu, Zhenzhong Wang, Dejun Xu, Kai Ye, Kay Chen Tan, Min Jiang
AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, experiments on three types of PDE are conducted to evaluate the performance of the proposed HD-TLGP. We evaluate the performance of the proposed HD-TLGP compared with traditional numerical method (FEM) (Multiphysics 1998), deep-learning based method (PINN) and GPSR based method (PR-GPSR) (Cao et al. 2023). |
| Researcher Affiliation | Academia | Lulu Cao1,2, Yufei Liu1,2, Zhenzhong Wang3, Dejun Xu1,2, Kai Ye1,2, Kay Chen Tan3, Min Jiang1,2* 1 School of Informatics, Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan, Ministry of Culture and Tourism, Xiamen University 2 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University 3 Department of Computing, The Hong Kong Polytechnic University |
| Pseudocode | Yes | Algorithm 1: Establishing a Transferred Knowledge Base Input: f s (The analytic solution of 1D PDE ), d (dimension of high-dimensional PDE) Output: knowledge base |
| Open Source Code | Yes | Code of this project is at https://github.com/grassdeerdeer/HD-TLGP. |
| Open Datasets | No | The paper defines the PDEs used for testing (Heat, Poisson, Advection equations) by their mathematical forms and conditions (Table 1), which are problem definitions rather than traditional publicly available datasets with specific access information (links, repositories, or citations to data sources). |
| Dataset Splits | No | The paper mentions using an "observation dataset D (Xi, yi)" for evaluation but does not specify how this dataset is split into training, validation, and test sets (e.g., by percentages or sample counts) needed for reproducibility. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU models, CPU types, memory) used to run the experiments. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers (e.g., Python, PyTorch, or other libraries with their respective versions) that would be needed to replicate the experiments. |
| Experiment Setup | No | The "Experiment Settings" section describes the types of PDEs tested and the comparative methods, but it does not specify concrete hyperparameters (e.g., learning rate, batch size, number of epochs) or other system-level training settings for the models used. |