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math.NA2024
Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
Thivin Anandh, Divij Ghose, Himanshu Jain +3
This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convect…
math.NA2024
POD-ROM methods: from a finite set of snapshots to continuous-in-time approximations
Bosco Garcia-Archilla, Volker John, Julia Novo
This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis i…
math.NA2023
POD-ROMs for incompressible flows including snapshots of the temporal derivative of the full order solution: Error bounds for the pressure
Bosco García-Archilla, Volker John, Sarah Katz +1
Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the…