Differential Spectral Normalization (DSN) for PDE Discovery
Authors: Chi Chiu So, Tsz On Li, Chufang Wu, Siu Pang Yung9675-9684
AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Experiment In this section, we compare DSN against 5 other settings: (1) symmetric finite difference filters (F), (2) momentconstrained filters without regularization (M), (3) spectral normalization (SN), (4) Weight decay (WD) as weight normalization and jacobian regularization both degenerate to WD, and (5) Orthonormal regularization (OR) on a 1D nonlinear PDE, namely, Korteweg-de Vries (Kd V) equation, and a 2D linear PDE, namely, confection-diffusion equation respectively. To allow comparability, the implementation of SN, WD and OR are all adjusted with reference to theorem 1 to allow their trainings to proceed on the space of moment tensor. |
| Researcher Affiliation | Academia | Chi Chiu So, Tsz On Li, Chufang Wu, Siu Pang Yung The University of Hong Kong kelccso@connect.hku.hk, toli2@cs.hku.hk, wucf@connect.hku.hk, spyung@hku.hk |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found in the paper. |
| Open Source Code | No | The paper does not provide an explicit statement or link indicating the availability of source code for the described methodology. |
| Open Datasets | No | The paper describes how the train-set was generated (e.g., "The initial condition for the Kd V equation is u0 = λ cos(x)...") but does not provide concrete access information (link, DOI, repository, or citation) for a publicly available or open dataset. |
| Dataset Splits | No | The paper mentions 'Train-set' and 'Test-set' but does not explicitly specify a 'validation' set or provide specific dataset split percentages or sample counts for training, validation, and testing. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory, cloud instances) used for running the experiments were found in the paper. |
| Software Dependencies | No | The paper does not provide specific software dependency details with version numbers (e.g., Python 3.8, PyTorch 1.9) required to replicate the experiments. |
| Experiment Setup | Yes | The batch size is 12. Adam (Kingma and Ba 2014) is used as the optimizer. For both PDEs, we set two separate scenarios with different noise magnitudes. Noise is added to train-set by ˆ ut = ut + [max ( ut) min ( ut)] µ (24) where max and min is the spatial maximum and minimum respectively. We set µ N(0, 0.01) and µ N(0, 0.05) in scenario 1 and 2 respectively. |