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..
PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling
Authors: Minju Jo, Woojin Cho, Uvini Balasuriya Mudiyanselage, Seungjun Lee, Noseong Park, Kookjin Lee
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through empirical studies on diverse scientific problems, we demonstrate that our method not only improves representational quality but also shows potential for forward and inverse inference tasks without the need for retraining. In this section, we empirically evaluate the proposed GFM and PDEfuncta frameworks. Our experiments focus on four main goals: (i) validating GFM s ability to compress and reconstruct PDE solution fields under single-INR modulation; (ii) evaluating whether the learned latent space enables generalization to unseen parameter configurations; (iii) demonstrating PDEfuncta s ability to perform bidirectional inference across paired function spaces; and (iv) comparing PDEfuncta against neural operator baselines on complex geometry benchmarks. |
| Researcher Affiliation | Collaboration | 1Sorbonne University, 2Tele PIX, 3SCAI, Arizona State University, 4Brookhaven National Laboratory, 5KAIST EMAIL, EMAIL, EMAIL, EMAIL, EMAIL, EMAIL |
| Pseudocode | Yes | In this section, we outline the meta-learning-based training and inference procedures for PDEfuncta. Algorithm 1 describes both the training and inference phase, where both network parameters and sample-specific latent vectors are jointly optimized via a nested inner outer loop. Algorithm 1 Training and Inference of the proposed method |
| Open Source Code | Yes | 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: [Yes] Justification: Data and code used in experiments are publicly available with explicit instructions included in supplementary materials. |
| Open Datasets | Yes | 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: [Yes] Justification: Data and code used in experiments are publicly available with explicit instructions included in supplementary materials. To assess capability of PDEfuncta for bidirectional inference, we use the Open FWI dataset [10], which contains pairs of samples across two distinct function spaces. |
| Dataset Splits | Yes | Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [Yes] Justification: Experimental setup and details, including data splits, hyperparameter, training algorithm are provided in main paper and Appendix D, I. In our experimentation, we use a total of 1,000 training data samples and 200 test data samples. |
| Hardware Specification | Yes | Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments? Answer: [Yes] Justification: Experimental setup and computer resources details are given in Appendix E. Experiments are conducted on a system running UBUNTU 18.04 LTS, PYTHON 3.9.7, PYTORCH 1.13.0, CUDA 11.6, i9 CPU, and NVIDIA RTX A5000. |
| Software Dependencies | Yes | Experiments are conducted on a system running UBUNTU 18.04 LTS, PYTHON 3.9.7, PYTORCH 1.13.0, CUDA 11.6, i9 CPU, and NVIDIA RTX A5000. |
| Experiment Setup | Yes | Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results? Answer: [Yes] Justification: Experimental setup and details, including data splits, hyperparameter, training algorithm are provided in main paper and Appendix D, I. For all experiments, we fixed the backbone INR to SIREN... we set ηinner = 0.01 and ηouter = 0.0001. All networks use a total of 5 layers, each with hidden dimension M = 256. The modulation mapping is implemented as a two-layer MLP with hidden dimension 512, and the dimension of the latent code z is fixed to 20 for all settings. ... The batch size and the number of training epochs for each dataset are as follows: batch size 32 and epoch 1,000 for Convection, batch size 16 and epoch 5,000 for Helmholtz, bach size 32 and epoch 5,000 for Kuramoto-Sivashinsky, batch size 10 and epoch 1,000 for Navier-Stokes, and batch size 16 and epoch 10,000 for FWI. |