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 and Learning Partial Differential Equations with Variational Q-Exponential Processes
Authors: Guangting Yu, Shiwei Lan
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through a series of experiments, including the Eikonal equation, Burgers equation, and an inverse Darcy flow problem, we demonstrate that the variational Q-EP method consistently yields more accurate solutions while providing meaningful uncertainty estimates. |
| Researcher Affiliation | Academia | Guangting Yu Shiwei Lan School of Mathematical & Statistical Sciences Arizona State University, Tempe, AZ 85287 EMAIL |
| Pseudocode | No | The paper describes methods and procedures in paragraph text, but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | The computer codes are publicly available at https://github.com/ lanzithinking/Diff_QEP. |
| Open Datasets | No | The paper mentions using 'FNO-Darcy data ... available in NVIDIA Physics Ne Mo' for one experiment, but does not provide a concrete link, DOI, specific repository name, or formal citation to access this dataset. Other data used are generated synthetically. |
| Dataset Splits | No | The paper describes using collocation points and randomly sampled observation points for training the PDE solvers, but does not provide explicit training/test/validation dataset splits with percentages or counts for a fixed dataset. |
| Hardware Specification | No | The paper does not explicitly mention specific hardware details (e.g., GPU/CPU models, memory amounts) used for running the experiments. |
| Software Dependencies | No | The paper mentions using 'python package GPy Torch [11] implemented based on Py Torch' but does not specify version numbers for these software components. |
| Experiment Setup | Yes | In most experiments, we choose the interior collocation points on a 24x24 mesh grid and the corresponding 100 boundary collocation points unless otherwise stated. For the sparse variational inference, M = 256 inducing points are randomly initialized and learned by optimizing the ELBO (9)... We train each algorithm for 5000 iterations... The kernel C of Q-EP/GP is chosen to be matern52 with the hyperparameters, e.g. the correlation strength, automatically tuned... |