Component Fourier Neural Operator for Singularly Perturbed Differential Equations
Authors: Ye Li, Ting Du, Yiwen Pang, Zhongyi Huang
AAAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results across diverse classes of SPDEs demonstrate that Com FNO significantly improves accuracy compared to vanilla FNO. Furthermore, Com FNO exhibits natural adaptability to diverse data distributions and performs well in few-shot scenarios, showcasing its excellent generalization ability in practical situations. |
| Researcher Affiliation | Academia | 1Nanjing University of Aeronautics and Astronautics 2Tsinghua University |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statement about open-sourcing the code or a link to a code repository. |
| Open Datasets | No | The paper describes generating its own training data ('The training dataset consists of 900 201 tuples (f, u), with 900 f samples independently drawn from Gaussian random fields and used as inputs. Resolution on [0, 1] or [ 1, 1] is fixed at 201. To derive u, we use high-precision numerical methods. For steady-state problems, which are independent of time, the upwind scheme on the Shishkin mesh is employed. For time-dependent problems, the Crank Nicolson scheme on the Shishkin mesh is used (Roos, Stynes, and Tobiska 2008).') but does not state that this generated dataset is publicly available or provide access information. |
| Dataset Splits | No | The paper mentions training and testing sets, but it does not specify a separate validation dataset or its split details. |
| Hardware Specification | No | The paper does not explicitly describe the specific hardware (e.g., GPU models, CPU types, memory) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies or libraries used in the experiments. |
| Experiment Setup | Yes | Subsequently, we detail the default experimental setup, where, unless explicitly stated, experiment parameters are established as follows. The parameter ε in SPDEs remains set at 1 10 3. Our aim is to learn the mapping f 7 u, where f represents the source term. The training dataset consists of 900 201 tuples (f, u), with 900 f samples independently drawn from Gaussian random fields and used as inputs. Resolution on [0, 1] or [ 1, 1] is fixed at 201. |