130 citations · 579 across the 34 of their papers we have counts for
35 papers
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…
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…
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition
Simone Brivio, Stefania Fresca, Nicola Rares Franco +1
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differentia…
Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression
Ludovica Cicci, Stefania Fresca, Mengwu Guo +2
Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving t…
Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions
Paolo Conti, Giorgio Gobat, Stefania Fresca +2
Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, whi…
Multi-fidelity surrogate modeling using long short-term memory networks
Paolo Conti, Mengwu Guo, Andrea Manzoni +1
When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for para…
Approximation bounds for convolutional neural networks in operator learning
Nicola Rares Franco, Stefania Fresca, Andrea Manzoni +1
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy…
A reduced order model for domain decompositions with non-conforming interfaces
Elena Zappon, Andrea Manzoni, Paola Gervasio +1
In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods.…
Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches
Giorgio Gobat, Stefania Fresca, Andrea Manzoni +1
Micro-Electro-Mechanical-Systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless app…
Robust optimal density control of robotic swarms
Carlo Sinigaglia, Andrea Manzoni, Francesco Braghin +1
In this paper, we propose a computationally efficient, robust density control strategy for the mean-field model of a robotic swarm. We formulate a static optimal control problem (O…
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…
Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces
Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical op…
Indirect Optimal Control of Advection-Diffusion Fields through Robotic Swarms
Carlo Sinigaglia, Andrea Manzoni, Francesco Braghin +1
In this paper, we consider the problem of optimally guiding a large-scale swarm of underwater vehicles that is tasked with the indirect control of an advection-diffusion environmen…
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…
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-…
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…
Deep learning-based reduced order models for the real-time simulation of the nonlinear dynamics of microstructures
Stefania Fresca, Giorgio Gobat, Patrick Fedeli +2
We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlineari…
Fast active thermal cloaking through PDE-constrained optimization and reduced-order modeling
Carlo Sinigaglia, Davide Enrico Quadrelli, Andrea Manzoni +1
In this paper we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources.…
Reduced order modeling of nonlinear microstructures through Proper Orthogonal Decomposition
Gobat G., Opreni A., Fresca S. +2
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites o…
Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
Stefania Fresca, Andrea Manzoni
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite eleme…
Density control of large-scale particles swarm through PDE-constrained optimization
Carlo Sinigaglia, Andrea Manzoni, Francesco Braghin
We describe in this paper an optimal control strategy for shaping a large-scale swarm of particles using boundary global actuation. This problem arises as a key challenge in many s…
Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks
Matteo Salvador, Luca Dede', Andrea Manzoni
We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition…
Online structural health monitoring by model order reduction and deep learning algorithms
Luca Rosafalco, Matteo Torzoni, Andrea Manzoni +2
Within a structural health monitoring (SHM) framework, we propose a simulation-based classification strategy to move towards online damage localization. The procedure combines para…
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations
Nicola R. Franco, Andrea Manzoni, Paolo Zunino
Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map.…