Robust Low-Rank Discovery of Data-Driven Partial Differential Equations
Authors: Jun Li, Gan Sun, Guoshuai Zhao, Li-wei H. Lehman767-774
AAAI 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Results from several experiments on seven canonical models (i.e., four PDEs and three parametric PDEs) verify that our framework outperforms the state-of-art sparse and group sparse regression methods. |
| Researcher Affiliation | Collaboration | Jun Li,1,2 Gan Sun,2 Guoshuai Zhao,2 Li-wei H. Lehman2,3 1School of Computer Science & Engineering, Nanjing University of Science and Technology, Nanjing, China 2Institute for Medical Engineering & Science, MIT, Cambridge, MA, USA 3MIT-IBM Watson AI Lab, Cambridge, MA, USA |
| Pseudocode | Yes | Algorithm 1 r PCA; Algorithm 2 Low-rank S(G)TRidge (Lr STR).; Algorithm 3 Double Low-rank Sparse Regression (DLr SR) |
| Open Source Code | Yes | Code is available at https://github.com/junli2019/Robust-Discovery-of-PDEs |
| Open Datasets | No | The paper describes generating data by numerically solving canonical PDEs rather than using pre-existing, publicly available datasets. For example, 'we numerically solve all parametric PDEs by employing the discrete Fourier transform (DFT) to evaluate spatial derivatives and using the Sci Py function odeint (Jones et al. 2001 ) for temporal integration with n and m.' |
| Dataset Splits | No | The paper does not provide specific details on training, validation, and test splits for the data used in the experiments. It describes data generation and noise addition, but not data partitioning for model training/evaluation. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., exact GPU/CPU models, memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions 'Sci Py function odeint (Jones et al. 2001 )' but does not provide specific version numbers for SciPy or any other software dependencies, such as the Python interpreter or other libraries used in the implementation. |
| Experiment Setup | No | The paper states: 'Due to the limited space, the hyper-parameter settings (i.e., λ1-λ4) are provided in the supplementary material.' Therefore, specific experimental setup details are not present in the main text. |