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Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

Published Online: 2026-06-02

Published Print: 2026-07

Authors

Geng, Yuwei

Yin, Junqi

Cyr, Eric C.

Zhang, Guannan

Ju, Lili https://orcid.org/0000-0002-6520-582X
Funding

Funding for this research was provided by:

U.S. Department of Energy (ERKJ388)

U.S. Department of Energy (ERKJ443)

U.S. Department of Energy (DE-SC0025527)
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Text and Data Mining valid from 2026-06-02

Version of Record valid from 2026-06-02
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Article History

Received: 29 September 2025

Revised: 4 May 2026

Accepted: 18 May 2026

First Online: 2 June 2026

Declarations

:

: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.

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