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Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs

Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex …

Simone Brivio, Stefania Fresca, Andrea Manzoni

On latent dynamics learning in nonlinear reduced order modeling

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized …

Nicola Farenga, Stefania Fresca, Simone Brivio, Andrea Manzoni

On latent dynamics learning in nonlinear reduced order modeling

PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs

Among several recently proposed data-driven Reduced Order Models (ROMs), the coupling of Proper Orthogonal Decomposition (POD) and deep …

Simone Brivio, Stefania Fresca, Andrea Manzoni

PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs

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