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..

Solving Partial Differential Equations via Radon Neural Operator

Authors: Wenbin Lu, Yihan Chen, Junnan Xu, Wei Li, Junwei Zhu, Jianwei Zheng

NeurIPS 2025 | Venue PDF | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Extensive experiments demonstrate that RNO sets new state-of-the-art (SOTA) scores across massive standard benchmarks, with superior generalization performance enjoyed. Code is available at https://github.com/wenbin-lu/Radon-Neural-Operator.
Researcher Affiliation Academia Wenbin Lu Yihan Chen Junnan Xu Wei Li Junwei Zhu Jianwei Zheng Zhejiang University of Technology, Hangzhou, Zhejiang
Pseudocode No The paper describes the methodology using mathematical equations (e.g., Eq. 3, 4, 5, 6, 7, 9) and architectural diagrams (Figures 3, 4, 5), but does not include any explicit pseudocode or algorithm blocks.
Open Source Code Yes Code is available at https://github.com/wenbin-lu/Radon-Neural-Operator.
Open Datasets Yes Standard Benchmarks. To better compare with existing work, we performed experiments on several publicly available benchmarks, including Plasticity, Airfoil, Pipe with structured mesh and Navier-Stokes, Darcy, Allen-Cahn with regular grid. These benchmark datasets were extensively investigated in seminal works such as FNO [23], geometry-aware FNO (geo-FNO) [22], and WNO [37], and have since gained widespread adoption in the scientific machine learning community.
Dataset Splits Yes Table 7: Summary of experiment benchmarks, where the first six datasets are from FNO and geo-FNO. Geometry Benchmarks Dim Mesh Input Output Dataset Structured Mesh Plasticity 2D+Time 3,131 External Force Mesh Displacement (900, 80) Airfoil 2D 11,271 Structure Mach Number (1000, 200) Pipe 2D 16,641 Structure Fluid Velocity (1000, 200) Regular Grid Navier Stokes 2D+Time 4,096 Past Velocity Future Velocity (1000, 200) Darcy 2D 7,225 Porous Medium Fluid Pressure (1000, 200) Allen-Cahn 2D 129 129 Initial Phase Field Evolved Phase Field (1000, 200)
Hardware Specification Yes For fairness, all experiments are consistently conducted on a standardized platform with an NVIDIA GTX 4090 GPU and 2.10GHz Intel(R) Xeon(R) Platinum 8352V CPU.
Software Dependencies No The paper mentions using 'Py Torch Fourier transform' and the 'ADAM [17] optimizer' but does not specify version numbers for PyTorch or any other software libraries. Section 4.3 mentions 'GPU-accelerated Py Torch Fourier transform'.
Experiment Setup Yes All competing methods are trained with l2 loss and 500 epochs. The ADAM [17] optimizer with an initial learning rate of 10 3 is used. For Radon transform, the main hyperparameters lie in the number of Radon blocks and the employed quantity of angles. Table 8: Training and model configurations of RNO. Here Lv and Ls represent the loss on volume and surface fields respectively. As for Darcy, we adopt an additional spatial gradient regularization term Lg following ONO [44]. Loss: Relative L2 [26], Epochs: 500, Initial LR: 10-3, Optimizer: AdamW. Model Configuration includes: Layers, Heads, Channels, Angles, Blocks for each benchmark.