Interpretable Solutions for Multi-Physics PDEs Using T-NNGP
Authors: Lulu Cao, Zexin Lin, Kay Chen Tan, Min Jiang
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results on three types of PDEs demonstrate that our method can reliably obtain human-understandable symbolic expressions that fit both the PDEs and the numerical solutions from traditional methods. This work advances multiphysics simulation by enhancing our ability to derive approximate symbolic solutions for PDEs, thereby improving our understanding of complex physical phenomena. In this section, experiments on three types of systems of PDEs are conducted to evaluate the performance of the proposed T-NNGP. |
| Researcher Affiliation | Academia | Lulu Cao1,2, 3, Zexin Lin1,2, Kay Chen Tan3, Min Jiang1,2* 1 Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China, Xiamen University 2 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 3 Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University |
| Pseudocode | Yes | Algorithm 1: T-NNGP Input: pdes (A system of PDEs to be solved), cu0 (the degree of constraint on each unknown function), f (Fitness function) Output: T (Optimal symbolic expression solutions) |
| Open Source Code | Yes | Code https://github.com/grassdeerdeer/T-NNGP |
| Open Datasets | No | In this paper, the physical dataset is generated by solving the systems of PDEs utilising the finite element method (FEM) (Permann et al. 2020; Li and Chen 2019). |
| Dataset Splits | Yes | For the symbolic regression method (Phy SO and TNNGP), 100 data points are randomly selected to generate expression. For Deep M&Mnet, 10% of the dataset is taken as training data. Compared to the entire dataset, very little data is used for training, so we use all the data in the dataset for evaluation. |
| Hardware Specification | No | No specific hardware details (like GPU/CPU models or specific cloud resources) were mentioned in the paper for running experiments. |
| Software Dependencies | No | The paper mentions methods like deep reinforcement learning, recursive neural networks (RNN), and genetic programming, but does not provide specific version numbers for any software libraries, frameworks, or languages used. |
| Experiment Setup | No | The paper states, "Table 3 in Appendix D lists the main parameters setting of T-NNGP." However, the content of Appendix D, including Table 3, is not provided in the main text of the paper. |