000132810 001__ 132810
000132810 005__ 20250923084412.0
000132810 0247_ $$2doi$$a10.1016/j.jcp.2024.112762
000132810 0248_ $$2sideral$$a137730
000132810 037__ $$aART-2024-137730
000132810 041__ $$aeng
000132810 100__ $$aPichi, Federico
000132810 245__ $$aA graph convolutional autoencoder approach to model order reduction for parametrized PDEs
000132810 260__ $$c2024
000132810 5060_ $$aAccess copy available to the general public$$fUnrestricted
000132810 5203_ $$aThe present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations of parametric Partial Differential Equations (PDEs). Linear techniques such as Proper Orthogonal Decomposition (POD) and Greedy algorithms have been analyzed thoroughly, but they are more suitable when dealing with linear and affine models showing a fast decay of the Kolmogorov n-width. On one hand, the autoencoder architecture represents a nonlinear generalization of the POD compression procedure, allowing one to encode the main information in a latent set of variables while extracting their main features. On the other hand, Graph Neural Networks (GNNs) constitute a natural framework for studying PDE solutions defined on unstructured meshes. Here, we develop a non-intrusive and data-driven nonlinear reduction approach, exploiting GNNs to encode the reduced manifold and enable fast evaluations of parametrized PDEs. We show the capabilities of the methodology for several models: linear/nonlinear and scalar/vector problems with fast/slow decay in the physically and geometrically parametrized setting. The main properties of our approach consist of (i) high generalizability in the low-data regime even for complex behaviors, (ii) physical compliance with general unstructured grids, and (iii) exploitation of pooling and un-pooling operations to learn from scattered data.
000132810 536__ $$9info:eu-repo/grantAgreement/ES/MICINN-AEI/PID2020-113463RB-C31/AEI/10.13039/501100011033$$9info:eu-repo/grantAgreement/ES/UZ-IBERCAJA-CAI/IT1-21
000132810 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000132810 590__ $$a3.8$$b2024
000132810 592__ $$a1.685$$b2024
000132810 591__ $$aPHYSICS, MATHEMATICAL$$b2 / 61 = 0.033$$c2024$$dQ1$$eT1
000132810 593__ $$aApplied Mathematics$$c2024$$dQ1
000132810 591__ $$aCOMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS$$b65 / 175 = 0.371$$c2024$$dQ2$$eT2
000132810 593__ $$aComputational Mathematics$$c2024$$dQ1
000132810 593__ $$aPhysics and Astronomy (miscellaneous)$$c2024$$dQ1
000132810 593__ $$aModeling and Simulation$$c2024$$dQ1
000132810 593__ $$aNumerical Analysis$$c2024$$dQ1
000132810 593__ $$aComputer Science Applications$$c2024$$dQ1
000132810 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000132810 700__ $$0(orcid)0000-0001-5483-6012$$aMoya, Beatriz
000132810 700__ $$aHesthaven, Jan S.
000132810 773__ $$g501 (2024), 112762 [24 pp.]$$pJ. comput. phys.$$tJournal of Computational Physics$$x0021-9991
000132810 8564_ $$s6353001$$uhttps://zaguan.unizar.es/record/132810/files/texto_completo.pdf$$yVersión publicada
000132810 8564_ $$s1915453$$uhttps://zaguan.unizar.es/record/132810/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000132810 909CO $$ooai:zaguan.unizar.es:132810$$particulos$$pdriver
000132810 951__ $$a2025-09-22-14:30:37
000132810 980__ $$aARTICLE