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 [1].
A Bregman Proximal Viewpoint on Neural Operators
Authors: Abdel-Rahim Mezidi, Jordan Patracone, Saverio Salzo, Amaury Habrard, Massimiliano Pontil, Rémi Emonet, Marc Sebban
ICML 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical experiments support the added benefits of the Bregman variant of Fourier neural operators for training deeper and more accurate models. [...] 5. Numerical Experiments The primary objective of our numerical experiments is to evaluate and assess the added benefits of the Bregman variant of the simplest neural operator, namely Fourier Neural Operator (FNO), and its improvements, as they often serve as the building blocks for more sophisticated models. |
| Researcher Affiliation | Academia | 1Université Jean Monnet Saint-Etienne, CNRS, Institut d Optique Graduate School, Inria, Laboratoire Hubert Curien UMR 5516, F-42023, SAINT-ETIENNE, France 2DIAG, Sapienza University of Rome, 00185 Rome, Italy 3Institut Universitaire de France (IUF) 4Computational Statistics and Machine Learning, IIT, Genova, Italy 5Departement of Computer Science, UCL, London, United Kingdom. |
| Pseudocode | No | The paper does not contain a dedicated section or figure labeled 'Pseudocode' or 'Algorithm'. |
| Open Source Code | Yes | The source code of this work is available on: https://github.com/armezidi/bregmano. |
| Open Datasets | Yes | We have selected a range of benchmark datasets resulting from the resolution of PDEs used both in the original FNO paper (Li et al., 2021a) and in the PDEBench suite (Takamoto et al., 2022), which is the top leading repository providing datasets commonly studied in physics-based machine learning. |
| Dataset Splits | Yes | If not mentioned otherwise, we use 8000 (resp. 1000) training samples for 1D (resp. 2D) problems, and 1000 samples each for validation and testing. All results are averaged over four random splittings. |
| Hardware Specification | No | Experiments have been made on an internal clusters of GPUs with memory from 10Go to 45Go. All the experiments can be achieved with GPUs with a memory of 10Go, except for models with 32 or 64 layers which require at least a memory of 24Go. The paper does not provide specific GPU/CPU models or other detailed hardware specifications. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers). |
| Experiment Setup | Yes | Models are trained using the Adam optimizer with a constant learning rate, a batch size of 128 for 1D problems (resp. 16 for 2D problems), a maximum of 2000 epochs and an early stopping strategy with patience of 250 epochs and δ = 10 3. The learning rate is validated on a grid of multiple values equally spaced in logarithmic scale. [...] we use the Re LU activation for FNO while, for BFNO, we resort to an invertible approximation: Soft Plus with parameter β = 103 to make it almost indistinguishible from Re LU. Hereafter, we consider models made of T {4, 8, 16, 32, 64} Fourier layers with a width 64 (resp. 32) and 16 (resp. 12) maximum number of Fourier modes for 1D (resp. 2D) problems. |