000164041 001__ 164041
000164041 005__ 20251121161351.0
000164041 0247_ $$2doi$$a10.1016/j.cma.2025.118476
000164041 0248_ $$2sideral$$a146303
000164041 037__ $$aART-2025-146303
000164041 041__ $$aeng
000164041 100__ $$aTesán, Lucas$$uUniversidad de Zaragoza
000164041 245__ $$aOn the under-reaching phenomenon in message passing neural PDE solvers: Revisiting the CFL condition
000164041 260__ $$c2025
000164041 5060_ $$aAccess copy available to the general public$$fUnrestricted
000164041 5203_ $$aThis paper proposes sharp lower bounds for the number of message passing iterations required in graph neural networks (GNNs) when solving partial differential equations (PDE). This significantly reduces the need for exhaustive hyperparameter tuning. Bounds are derived for the three fundamental classes of PDEs (hyperbolic, parabolic and elliptic) by relating the physical characteristics of the problem in question to the message-passing requirement of GNNs. In particular, we investigate the relationship between the physical constants of the equations governing the problem, the spatial and temporal discretisation and the message passing mechanisms in GNNs. When the number of message passing iterations is below these proposed limits, information does not propagate efficiently through the network, resulting in poor solutions, even for deep GNN architectures. In contrast, when the suggested lower bound is satisfied, the GNN parameterisation allows the model to accurately capture the underlying phenomenology, resulting in solvers of adequate accuracy. Examples are provided for four different examples of equations that show the sharpness of the proposed lower bounds.
000164041 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2023-147373OB-I00$$9info:eu-repo/grantAgreement/ES/MTFP/TSI-100930-2023-1
000164041 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
000164041 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000164041 700__ $$aMartínez Iparraguirre, Mikel$$uUniversidad de Zaragoza
000164041 700__ $$0(orcid)0000-0003-3003-5856$$aGonzález, David$$uUniversidad de Zaragoza
000164041 700__ $$0(orcid)0000-0001-9732-4498$$aLopes De Sousa Martins, Pedro
000164041 700__ $$0(orcid)0000-0003-1017-4381$$aCueto, Elías$$uUniversidad de Zaragoza
000164041 7102_ $$15004$$2605$$aUniversidad de Zaragoza$$bDpto. Ingeniería Mecánica$$cÁrea Mec.Med.Cont. y Teor.Est.
000164041 773__ $$g449 (2025), 118476 [17 pp.]$$pComput. methods appl. mech. eng.$$tComputer Methods in Applied Mechanics and Engineering$$x0045-7825
000164041 8564_ $$s7153362$$uhttps://zaguan.unizar.es/record/164041/files/texto_completo.pdf$$yVersión publicada
000164041 8564_ $$s1948703$$uhttps://zaguan.unizar.es/record/164041/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000164041 909CO $$ooai:zaguan.unizar.es:164041$$particulos$$pdriver
000164041 951__ $$a2025-11-21-14:25:20
000164041 980__ $$aARTICLE