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..
SpiderSolver: A Geometry-Aware Transformer for Solving PDEs on Complex Geometries
Authors: KAI QI, Fan Wang, Zhewen Dong, Jian Sun
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate Spider Solver on PDEs with diverse domain geometries across seven datasets, including cars, airfoils, blood flow in the human thoracic aorta, as well as canonical cases governed by the Navier-Stokes, Darcy flow, elasticity, and plasticity equations. Experimental results demonstrate that Spider Solver consistently achieves state-of-the-art performance across different datasets and metrics, with better generalization ability in the OOD setting. |
| Researcher Affiliation | Academia | Kai Qi1,*, Fan Wang1,*, Zhewen Dong1, Jian Sun1,2 (B) 1School of Mathematics and Statistics, Xi an Jiaotong University, Xi an, China 2State Industry-Education Integration Center for Medical Innovations at Xi an Jiaotong University EMAIL, EMAIL |
| Pseudocode | No | The paper describes the architecture and methods in detail in Section 3 and its subsections, but it does not present any formal pseudocode or algorithm blocks. It explains processes like Spiderweb Tokenization and the Transformer Design, but without structured algorithm formatting. |
| Open Source Code | Yes | The code is available at https://github.com/Kai-Qi/Spider Solver. |
| Open Datasets | Yes | We evaluate Spider Solver on five datasets spanning industrial, biomedical, and fundamental PDE tasks... Shape-Net Car [33]... Airf RANS [35]... Blood Flow dataset [36]... Bounded Navier-Stokes dataset with multiple separate boundaries [37]... Darcy Flow dataset [3]... Elasticity [6] models... Plasticity [6] considers... |
| Dataset Splits | Yes | Shape-Net Car [33] consists of 889 simulated samples... 789 samples are used for training, and the other 100 samples are for testing... Airf RANS [35] comprises 1,000 high-fidelity simulations... 720 samples are used for training, 80 samples are used for validation, and 200 for the test set. Blood Flow dataset [36]... 400 samples are used as training data, 50 samples are used as validation data and the remaining 50 as test data... Bounded Navier-Stokes dataset... A total of 1,000 training sequences, 200 validation sequences and 200 test sequences are used at a spatial resolution of 64 64. Darcy Flow dataset [3]... We use 1000, 200, and 200 pairs of a(x) and u(x) in the train, validation, and test sets, respectively. |
| Hardware Specification | Yes | All experiments are performed on a Ge Force RTX 4090 GPU. |
| Software Dependencies | No | We employ standard Spectral Clustering function from the scikit-learn library, configured as follows: Spectral Clustering(n_clusters=clusters, affinity= nearest_neighbors , random_state=42). While scikit-learn is mentioned, no specific version number for this or any other software dependency is provided. |
| Experiment Setup | Yes | To ensure that our model parameters are comparable to other Transformer-based models, such as Transolver, we set the number of layers as 8 and the channel of hidden features as 256 or 512, depending on the number of observed quantities of input data... Table 9: Settings of hyper-parameters in the Spider Solver network and Spider Solver training. This table lists specific values for parameters like m I, m B, L, h, C, dk, Loss, Epochs, LR, Optimizer, and Batch Size for each dataset. |