Semi-Implicit Neural Ordinary Differential Equations
Authors: Hong Zhang, Ying Liu, Romit Maulik
AAAI 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate and evaluate the performance of our methods when learning stiff ODE systems. Throughout this section we compare our methods with a variety of baseline methods including explicit and implicit methods. The neural network architectures we use follow the best settings identified in previous works (Linot et al. 2022; Chamberlain et al. 2021). The only modification necessary for using our method is to split the ODE right-hand side. Code is available at https://github.com/caidao22/pnode. 5.1 Graph Classification with GRAND ... 5.2 Learning Dynamics for the Kuramoto Sivashinsky (KS) Equation ... 5.3 Learning Dynamics for the Viscous Burgers Equation |
| Researcher Affiliation | Academia | Hong Zhang 1, Ying Liu 2, Romit Maulik 1,3 1Argonne National Laboratory 2University of Iowa 3Pennsylvania State University EMAIL, EMAIL, EMAIL |
| Pseudocode | No | The paper describes the forward and backward passes using equations and detailed explanations, but does not present a structured pseudocode or algorithm block. |
| Open Source Code | Yes | Code is available at https://github.com/caidao22/pnode. |
| Open Datasets | Yes | For assessment, we choose three benchmark datasets: Cora, Coauthor CS, and Photo. |
| Dataset Splits | No | The paper mentions using benchmark datasets like Cora, Coauthor CS, and Photo, and refers to a 'testing dataset' for the viscous Burgers equation, but does not specify the training/validation/test splits used for these experiments. |
| Hardware Specification | No | The paper mentions using computing resources provided by the Joint Laboratory for System Evaluation (JLSE) at Argonne National Laboratory, but does not provide specific hardware details such as GPU/CPU models or memory amounts. |
| Software Dependencies | No | SINODE is implemented in the PNODE framework (Zhang and Zhao 2022) that integrates Py Torch and PETSc seamlessly. We have implemented these algorithms as off-the-shelf solvers in PETSc (Balay et al. 2023). |
| Experiment Setup | Yes | Because of the stability constraints, we have to utilize a step size of 0.005 for explicit methods, while the implicit methods and the IMEX methods allow us to use a step size of 1 thanks to their superior stability properties. A time step size 0.2 is used for the IMEX methods and the fully implicit method. ... we choose a time step size of 0.05 as a conservative choice for the four IMEXRK methods and the fully implicit method. |