October 15, 2024
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Article

A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers

Publicated to: Results in Engineering. 24 102949- - 2024-12-01 24(), DOI: 10.1016/j.rineng.2024.102949

Authors:

Huergo, D; Alonso, L; Joshi, S; Juanicotena, A; Rubio, G; Ferrer, E
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Affiliations

Univ Politecn Madrid, Ctr Computat Simulat, Campus Montegancedo, Madrid 28660, Spain - Author
Univ Politecn Madrid, Sch Aeronaut, ETSIAE UPM, Plaza Cardenal Cisneros 3, E-28040 Madrid, Spain - Author

Abstract

We explore a reinforcement learning strategy to automate and accelerate h/p-multigrid methods in high-order solvers. Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing sweeps per level and the correction fraction (i.e., proportion of the corrected solution that is transferred from a coarser grid to a finer grid). The objective of this paper is to use a proximal policy optimization algorithm to automatically tune the multigrid parameters and, by doing so, improve stability and efficiency of the h/p-multigrid strategy. Our findings reveal that the proposed reinforcement learning h/p-multigrid approach significantly accelerates and improves the robustness of steady-state simulations for one-dimensional advection-diffusion and nonlinear Burgers' equations, when discretized using high-order h/p methods, on uniform and nonuniform grids.
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Keywords

Advection-diffusionBurgers' equationH/p-multigriH/p-multigridHigh-order flux reconstructionPpoProximal policy optimizationReinforcement learning

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Results in Engineering due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 6/179, thus managing to position itself as a Q1 (Primer Cuartil), in the category Engineering, Multidisciplinary. Notably, the journal is positioned above the 90th percentile.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-07:

  • Google Scholar: 1
  • WoS: 3
  • Scopus: 3
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-07:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 5.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 5 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 2.
  • The number of mentions on the social network X (formerly Twitter): 2 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/86487/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 135
  • Downloads: 30
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Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (HUERGO PEREA, DAVID) and Last Author (FERRER VACCAREZZA, ESTEBAN).

the author responsible for correspondence tasks has been HUERGO PEREA, DAVID.

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Awards linked to the item

Gonzalo Rubio and Esteban Ferrer acknowledge the funding received by the Grant DeepCFD (Project No. PID2022-137899OB-I00) funded by MICIU/AEI/10.13039/501100011033 and ERDF, EU. This research has been cofunded by the European Union (ERC, Offcoustics, project number 101086075). Views and opinions expressed are, however, those of the author (s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Finally, all authors gratefully acknowledge the Universidad Politecnica de Madrid (http:// www.upm.es) for providing computing resources on Magerit Supercomputer.
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