Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs
Authors: Songming Liu, Hao Zhongkai, Chengyang Ying, Hang Su, Jun Zhu, Ze Cheng
NeurIPS 2022 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results on real-world geometrically complex PDEs showcase the effectiveness of our method compared with state-of-the-art baselines. We empirically demonstrate the effectiveness of our method through three parts of experiments. |
| Researcher Affiliation | Collaboration | 1Dept. of Comp. Sci. and Tech., Institute for AI, THBI Lab, BNRist Center, Tsinghua-Bosch Joint ML Center, Tsinghua University 2Peng Cheng Laboratory; Pazhou Laboratory (Huangpu), Guangzhou, China 3Bosch Center for Artificial Intelligence |
| Pseudocode | No | The paper describes its method using equations and textual descriptions but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] See the supplementary material. |
| Open Datasets | Yes | the 2D stationary incompressible Navier-Stokes equations, in the context of simulating the airflow around a real-world airfoil (w1015.dat) from the UIUC airfoil coordinates database (an open airfoil database) [29]. |
| Dataset Splits | No | The paper specifies the number of collocation points for training and testing, but does not explicitly mention a separate validation set or split percentages. |
| Hardware Specification | Yes | The total amount of compute is around 50 GPU hours with NVIDIA V100 GPU. |
| Software Dependencies | No | The paper states that the method is 'implemented in PyTorch' but does not provide specific version numbers for PyTorch or any other software dependencies. |
| Experiment Setup | Yes | We use Adam optimizer with a learning rate of 1e-3, and then use L-BFGS optimizer. The learning rate of Adam is decayed using cosine annealing schedule [29] (with a warm up of 1000 iterations). In each experiment, we sample Nf collocation points, Nb boundary points, and Ni initial points. |