Nearest Neighbors GParareal: Improving Scalability of Gaussian Processes for Parallel-in-Time Solvers
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Gattiglio, Guglielmo Grigoryeva, Lyudmila Tamborrino, Massimiliano |
| author_facet | Gattiglio, Guglielmo Grigoryeva, Lyudmila Tamborrino, Massimiliano |
| contents | With the advent of supercomputers, multi-processor 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nearest Neighbors GParareal: Improving Scalability of Gaussian Processes for Parallel-in-Time Solvers Gattiglio, Guglielmo Grigoryeva, Lyudmila Tamborrino, Massimiliano Computation Distributed, Parallel, and Cluster Computing Numerical Analysis 65M55, 65M22, 65L05, 50G15, 65Y05 With the advent of supercomputers, multi-processor 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). |
| title | Nearest Neighbors GParareal: Improving Scalability of Gaussian Processes for Parallel-in-Time Solvers |
| topic | Computation Distributed, Parallel, and Cluster Computing Numerical Analysis 65M55, 65M22, 65L05, 50G15, 65Y05 |
| url | https://arxiv.org/abs/2405.12182 |