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..
Neural Green’s Functions
Authors: Seungwoo Yoo, Kyeongmin Yeo, Jisung Hwang, Minhyuk Sung
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In our experiments, we first empirically validate the generalizability of the proposed framework using simple examples of the Poisson and Biharmonic equations. We then extend the evaluation to a practical setting of steady-state thermal analysis on complex 3D geometries, using a benchmark we built from the MCB dataset [16]. In comparisons, Neural Green s Function demonstrates superior generalizability compared to state-of-the-art neural operators, achieving an average error reduction of 13.9 % across five shape categories, while being up to 350 times faster than a numerical solver that requires computationally expensive meshing. |
| Researcher Affiliation | Academia | Seungwoo Yoo Kyeongmin Yeo Jisung Hwang Minhyuk Sung KAIST EMAIL |
| Pseudocode | No | The paper describes the methodology using mathematical equations and textual explanations, but it does not include a specific block labeled "Pseudocode" or "Algorithm" with structured, step-by-step instructions. |
| Open Source Code | No | Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [No] Justification: We plan to release the code and data required to reproduce the results upon acceptance. |
| Open Datasets | Yes | To this end, we construct a new PDE benchmark using the MCB dataset [16], which contains a variety of 3D mechanical part shapes. |
| Dataset Splits | Yes | The shape collection is divided into 200 shapes for training and 20 shapes for testing to evaluate generalization to unseen problem domains. ... Overall, the dataset comprises 3200 shape-problem pairs for training and 320 pairs for testing across all categories. |
| Hardware Specification | Yes | All runtimes are measured on a system equipped with an Intel Xeon Gold 6442Y processor with 24 cores and an NVIDIA RTX 3090 GPU with 24 GB of VRAM. |
| Software Dependencies | No | While the paper mentions several software tools like "f Tet Wild [14]", "libigl [15]", "Cholespy[1]", and an "FEM solver [11]" (Lapy), it does not provide specific version numbers for these software components. For example, it refers to "Lapy: Toolbox for differential geometry on triangle and tetrahedra meshes, 2023. URL https://github.com/Deep-MI/La Py." where 2023 is a year, not a version number. Similarly, Cholespy is referenced by name and URL, but no version. |
| Experiment Setup | Yes | Unless otherwise specified, all models in our experiments are trained for 40 epochs using the ADAM optimizer [17] with a One Cycle LR learning rate scheduler, setting the maximum learning rate to 1 10 4. For the steady-state thermal analysis experiments in Sec. 5.3, we use a batch size of 1 and accumulate gradients over 8 training steps to stabilize training, to handle meshes with a large number of vertices. |