Nearest Neighbors GParareal: Improving Scalability of Gaussian Processes for Parallel-in-Time Solvers
Guglielmo Gattiglio, Lyudmila Grigoryeva, Massimiliano Tamborrino
Source abstract
Abstract. With the advent of supercomputers, multiprocessor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial differential equations (ODEs and PDEs) over long time intervals, a task often unfeasible with sequential solvers within realistic time frames. A recent approach, GParareal, combines Gaussian Processes with traditional PinT methodology (Parareal) to achieve faster parallel speed-ups. The method is known to outperform Parareal for low-dimensional ODEs and a limited number of computer cores. Here, we present Nearest Neighbors GParareal (nnGParareal), a novel data-enriched PinT integration algorithm. nnGParareal builds upon GParareal by improving its scalability properties for higher-dimensional systems and increased processor count. Through data reduction, the model complexity is reduced from cubic to log-linear in the sample size, yielding a fast and automated procedure to integrate initial value problems over long time intervals. First, we provide both an upper bound for the error and theoretical details on the speed-up benefits. Then, we empirically illustrate the superior performance of nnGParareal compared to GParareal and Parareal on nine different systems with unique features (e.g., stiff, chaotic, high-dimensional, or challenging-to-learn systems). Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/Parallel-in-Time-Differential-Equations/Nearest-Neighbors-GParareal and in the supplementary materials ( nnGParareal_supplementary_material.pdf [2.53MB], Nearest-Neighbors-GParareal-main.zip [9.34MB]). [Formula: see text]
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.