PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers
Authors: Namgyu Kang, Byeonghyeon Lee, Youngjoon Hong, Seok-Bae Yun, Eunbyung Park
AAAI 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We provide experimental results on various challenging PDEs that the original PINNs have struggled with and show that PIXEL achieves fast convergence speed and high accuracy. |
| Researcher Affiliation | Academia | 1Department of Artificial Intelligence, Sungkyunkwan University 2Department of Mathematics, Sungkyunkwan University 3Department of Electrical and Computer Engineering, Sungkyunkwan University |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. |
| Open Source Code | Yes | You can find our customized CUDA kernel code at https://github.com/NamGyuKang/CosineSampler. |
| Open Datasets | No | The paper describes the PDEs and their conditions, but does not refer to publicly available datasets with access information or standard dataset names. |
| Dataset Splits | No | The paper does not specify dataset split percentages or counts for training, validation, or testing. |
| Hardware Specification | No | The paper does not specify any particular hardware (GPU, CPU models, etc.) used for the experiments. |
| Software Dependencies | No | The paper mentions using "automatic differentiation" (implying frameworks like PyTorch) and having "customized CUDA kernel code" but does not provide specific version numbers for any software dependencies. |
| Experiment Setup | Yes | For all experiments, we used Limited-memory BFGS (L-BFGS) second-order optimization algorithms. We run both PINN and PIXEL 5 times for each PDE experiment, and the shaded areas show 80% confidence interval of 5 different runs with different random seeds (100, 200, 300, 400, 500). For higher accuracy, we trained more iterations until convergence, 10k, 1k, 500k, 39k, 18k, and 10k iterations were performed for each PDE according to the sequence shown in the Table 2, respectively. |