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20172023
most citedA comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs

5 citations · 12 across the 11 of their papers we have counts for

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9 papers · 1 filter

math.NA20231 cited

A staggered-in-time and non-conforming-in-space numerical framework for realistic cardiac electrophysiology outputs

Elena Zappon, Andrea Manzoni, Alfio Quarteroni

Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to…

math.NA2023

Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks

Nicola Rares Franco, Stefania Fresca, Filippo Tombari +1

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-de…

math.NA2022

Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces

Elena Zappon, Andrea Manzoni, Alfio Quarteroni

One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains…

math.NA20221 cited

Efficient approximation of cardiac mechanics through reduced order modeling with deep learning-based operator approximation

Ludovica Cicci, Stefania Fresca, Andrea Manzoni +1

Reducing the computational time required by high-fidelity, full order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient…

math.NA20221 cited

Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs

Ludovica Cicci, Stefania Fresca, Andrea Manzoni

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-…

math.NA20224 cited

Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order models

Federico Fatone, Stefania Fresca, Andrea Manzoni

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper…