RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks
Authors: Guglielmo Gattiglio, Lyudmila Grigoryeva, Massimiliano Tamborrino
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Rand Net-Parareal s numerical performance is illustrated on systems of real-world significance, such as the viscous Burgers equation, the Diffusion-Reaction equation, the twoand three-dimensional Brusselator, and the shallow water equation. |
| Researcher Affiliation | Academia | Guglielmo Gattiglio Department of Statistics University of Warwick Coventry, CV4 7AL, UK Guglielmo.Gattiglio@warwick.ac.uk Lyudmila Grigoryeva Faculty of Mathematics and Statistics University of St. Gallen Rosenbergstrasse 20, CH-9000 St. Gallen, Switzerland Lyudmila.Grigoryeva@unisg.ch Massimiliano Tamborrino Department of Statistics University of Warwick Coventry, CV4 7AL, UK Massimiliano.Tamborrino@warwick.ac.uk |
| Pseudocode | Yes | A Parareal pseudocode is presented in Algorithm 1 in Supplementary Material A. |
| Open Source Code | Yes | Moreover, all simulation outcomes, including tables and figures, are fully reproducible and accompanied by the necessary Python code at https://github.com/Parallel-in-Time-Differential-Equations/Rand Net-Parareal. |
| Open Datasets | No | The paper describes generating initial conditions and spatial discretizations for PDE problems, which are not standard publicly available datasets with concrete access information (links, DOIs, or formal citations to existing datasets). |
| Dataset Splits | No | The paper does not provide specific training/validation/test dataset split information. The concept of 'training' refers to the Rand Nets learning the discrepancy within the Parareal algorithm, not traditional data splits for a machine learning model on a pre-existing dataset. |
| Hardware Specification | Yes | All experiments have been executed on Dell Power Edge C6420 compute nodes each with 2 x Intel Xeon Platinum 826 (Cascade Lake) 2.9 GHz 24-core processors, 48 cores and 192 GB DDR4-2933 RAM per node. |
| Software Dependencies | No | The paper mentions 'scipy Runge-Kutta method [77]' and 'Pararea ML [8] Python package' but does not specify their version numbers or the version of Python used. |
| Experiment Setup | Yes | The simulation setups used for obtaining the results in this section are provided in Supplementary Material G, with the corresponding accuracies and runtimes for Rand Net-Parareal, Parareal, and nn GParareal reported in Supplementary Material F. For example, Table 5, 6, and 7 provide detailed parameters such as Nx, Ny, d, G, NG, F, NF, N, mnn GP, and m Rand Net. |