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Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) …

Simone Brivio, Stefania Fresca, Nicola Rares Franco, Andrea Manzoni

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

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, …

Nicola Rares Franco, Stefania Fresca, Filippo Tombari, Andrea Manzoni

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

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

Ludovica Cicci, Stefania Fresca, Andrea Manzoni, Alfio Quarteroni

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

Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity …

Ludovica Cicci, Stefania Fresca, Mengwu Guo, Andrea Manzoni, Paolo Zunino

Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression

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

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional …

Stefania Fresca, Federico Fatone, Andrea Manzoni

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

Modeling the periodic response of Micro-Electromechanical Systems through deep learning-based approaches

We propose a deep learning-based reduced order modelling approach for micro-electromechanical systems. The method allows treating …

Giorgio Gobat, Alessia Baronchelli, Stefania Fresca, Attilio Frangi

Approximation bounds for convolutional neural networks in operator learning

Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling …

Nicola Rares Franco, Stefania Fresca, Andrea Manzoni, Paolo Zunino

Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods …

Paolo Conti, Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi

Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions

Reduced order modelling of nonlinear vibrating multiphysics microstructures with deep learning-based approaches

Micro-electro-mechanical-systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are …

Giorgio Gobat, Stefania Fresca, Andrea Manzoni, Attilio Frangi

Reduced order modelling of nonlinear vibrating multiphysics microstructures with deep learning-based approaches

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

To speed-up the solution of parametrized differential problems, reduced order models (ROMs) have been developed over the years, …

Ludovica Cicci, Stefania Fresca, Andrea Manzoni

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