Δ-PINNs: Physics-informed neural networks on complex geometries

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dc.article.number107324
dc.catalogadorgjm
dc.contributor.authorSahli Costabal, Francisco
dc.contributor.authorPezzuto, Simone
dc.contributor.authorPerdikaris, Paris
dc.date.accessioned2024-05-30T16:23:24Z
dc.date.available2024-05-30T16:23:24Z
dc.date.issued2024
dc.description.abstractPhysics-informed neural networks (PINNs) have demonstrated promise in solving forward and inverse problems involving partial differential equations. Despite recent progress on expanding the class of problems that can be tackled by PINNs, most of existing use-cases involve simple geometric domains. To date, there is no clear way to inform PINNs about the topology of the domain where the problem is being solved. In this work, we propose a novel positional encoding mechanism for PINNs based on the eigenfunctions of the Laplace–Beltrami operator. This technique allows to create an input space for the neural network that represents the geometry of a given object. We approximate the eigenfunctions as well as the operators involved in the partial differential equations with finite elements. We extensively test and compare the proposed methodology against different types of PINNs in complex shapes, such as a coil, a heat sink and the Stanford bunny, with different physics, such as the Eikonal equation and heat transfer. We also study the sensitivity of our method to the number of eigenfunctions used, as well as the discretization used for the eigenfunctions and the underlying operators. Our results show excellent agreement with the ground truth data in cases where traditional PINNs fail to produce a meaningful solution. We envision this new technique will expand the effectiveness of PINNs to more realistic applications. Code available at: https://github.com/fsahli/Delta-PINNs.
dc.fuente.origenORCID
dc.identifier.doi10.1016/j.engappai.2023.107324
dc.identifier.urihttps://doi.org/10.1016/j.engappai.2023.107324
dc.identifier.urihttp://www.scopus.com/inward/record.url?eid=2-s2.0-85175039285&partnerID=MN8TOARS
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/86068
dc.information.autorucEscuela de Ingeniería; Sahli Costabal, Francisco; S/I; 154857
dc.issue.numeroPart B
dc.language.isoen
dc.nota.accesocontenido parcial
dc.revistaEngineering Applications of Artificial Intelligence
dc.rightsacceso restringido
dc.subjectDeep learning
dc.subjectLaplace–Beltrami eigenfunctions
dc.subjectPhysics-informed neural networks
dc.subjectEikonal equation
dc.subjectPartial differential equations
dc.subject.ddc600
dc.subject.deweyTecnologíaes_ES
dc.titleΔ-PINNs: Physics-informed neural networks on complex geometries
dc.typeartículo
dc.volumen127
sipa.codpersvinculados154857
sipa.trazabilidadORCID;2024-05-27
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