- Available MOX Reports
- Theses
- Thesis Proposals
- MOX Projects

*Salvador, M.; Dede', L.; Manzoni, A.*

Non intrusive reduced order modeling of parametrized PDEs by kernel POD and neural networks

*Massi, M.c.; Franco, N.r; Ieva, F.; Manzoni, A.; Paganoni, A.m.; Zunino, P.*

High-Order Interaction Learning via Targeted Pattern Search

*Fresca, S.; Manzoni, A.; DedÃ¨, L.; Quarteroni, A.*

Deep learning-based reduced order models in cardiac electrophysiology

*Massi, M.c., Gasperoni, F., Ieva, F., Paganoni, A.m., Zunino, P., Manzoni, A., Franco, N.r., Et Al.*

A deep learning approach validates genetic risk factors for late toxicity after prostate cancer radiotherapy in a REQUITE multinational cohort

*Fresca, S.; Dede', L.; Manzoni, A.*

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

*Manzoni, A; Quarteroni, A.; Salsa, S.*

A saddle point approach to an optimal boundary control problem for steady Navier-Stokes equations

*Dal Santo, N.; Manzoni, A.*

Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape

*Pagani, S.; Manzoni, A.; Carlberg, K.*

Statistical closure modeling for reduced-order models of stationary systems by the ROMES method

*Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.*

Multi space reduced basis preconditioners for parametrized Stokes equations

*Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.*

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

*Manzoni, A; Bonomi, D.; Quarteroni, A.*

Reduced order modeling for cardiac electrophysiology and mechanics: new methodologies, challenges & perspectives

*Dal Santo, N.; Deparis, S.; Manzoni, A.; Quarteroni, A.*

Multi space reduced basis preconditioners for large-scale parametrized PDEs

*Pagani, S.; Manzoni, A.; Quarteroni, A.*

Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method

*Quarteroni, A.; Manzoni, A.; Vergara, C.*

The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications

*Pagani, S.; Manzoni, A.; Quarteroni, A.*

A Reduced Basis Ensemble Kalman Filter for State/parameter Identification in Large-scale Nonlinear Dynamical Systems

*Bonomi, D.; Manzoni, A.; Quarteroni, A.*

A matrix discrete empirical interpolation method for the efficient model reduction of parametrized nonlinear PDEs: application to nonlinear elasticity problems

*Ballarin, F.; Faggiano, E.; Ippolito, S.; Manzoni, A.; Quarteroni, A.; Rozza, G.; Scrofani, R.*

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD–Galerkin method and a vascular shape parametrization

*Manzoni, A.; Pagani, S.*

A certified reduced basis method for PDE-constrained parametric optimization problems by an adjoint-based approach

*Fumagalli, I.; Manzoni, A.; Parolini, N.; Verani, M.*

Reduced basis approximation and a posteriori error estimates for parametrized elliptic eigenvalue problems

*Manzoni, A.; Pagani, S.; Lassila, T. *

Accurate solution of Bayesian inverse uncertainty quantification problems using model and error reduction methods

*Ballarin, F.; Manzoni, A.; Quarteroni, A.; Rozza, G.*

Supremizer stabilization of POD-Galerkin approximation of parametrized Navier-Stokes equations

*Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.*

Model order reduction in fluid dynamics: challenges and perspectives

*Negri, F.; Rozza, G.; Manzoni, A.; Quarteroni, A.*

Reduced basis method for parametrized elliptic optimal control problems

*Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.*

Generalized reduced basis methods and n width estimates for the approximation of the solution manifold of parametric PDEs

*Manzoni, A.; Quarteroni, A.; Gianluigi Rozza, G.*

Computational reduction for parametrized PDEs: strategies and applications

*Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.*

Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

*Lassila, T.; Manzoni, A.; Quarteroni, A.; Rozza, G.*

A reduced computational and geometrical framework for inverse problems in haemodynamics

*Manzoni, A.; Quarteroni, A.; Rozza, G.*

Model reduction techniques for fast blood flow simulation in parametrized geometries

*Quarteroni, A.; Rozza, G.; Manzoni, A.*

Certified Reduced Basis Approximation for Parametrized Partial Differential Equations and Applications

*Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi*

Shape optimization for viscous flows by reduced basis methods and free-form deformation

Author:*Ratti, Luca*

Advisors:*Beretta, E. Manzoni, A.*

Un algoritmo di ricostruzione per la soluzione di un problema inverso al contorno per un'equazione ellittica semilineare

Author:*Manzoni, Andrea*

Advisors:*Salsa, S. Parolini, N. *

Ottimizzazione di forma per problemi di fluidodinamica: analisi teorica e metodi numerici

Author:*Conca, Alessandro; Manzoni, Andrea*

Advisors:*Saleri, Fausto *

Simulazione e controllo del rilascio di un inquinante nella laguna veneta

Forward Uncertainty Quantification for Dynamical Systems *
*

*Uncertainty quantification (UQ) can be defined as the science of identifying, quantifying, and reducing uncertainties associated with models, numerical algorithms, experiments, and predicted outcomes or quantities of interest. The thesis project aims at investigating new approaches to perform uncertainty propagation (from model inputs to time-dependent output quantities of interest) for nonlinear dynamical systems. Both sensitivity analysis and uncertainty propagation will be addressed, exploiting Monte Carlo techniques and suitable extensions (multi-level Monte Carlo techniques); numerical accuracy of the estimated quantities will be carefully assessed. As motivating example, we will start from recently proposed generalized SEIR models to describe the Covid-19 pandemic. This project is in collaboration with Dr. Lorenzo Tamellini (CNR-IMATI, Pavia).*

Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent problems

Highly accurate numerical or physical experiments are often very time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide satisfactory model results. Multi-fidelity methods deal with such problems by incorporating information from other sources, which are ideally well-correlated with the high-fidelity data, but can be obtained at a lower cost. Extending the strategies recently proposed in **arXiv:2102.1340**3, the goal of this project is to design and exploit new neural network architectures for multi-fidelity regression in engineering problems, involving the evaluation of output quantities of interest, as well as the solution of underlying differential problems. We expect to obtain outputs/solutions that achieve a comparable accuracy to those from the expensive, full-order model, using only very few full-order evaluations combined with a larger amount of inaccurate but cheap evaluations of a reduced order model.

Physics-informed machine learning and data-driven discovery of dynamical systems

Dynamical systems models are ubiquitous tools used to study, explain, and predict system behavior in a wide range of application areas. The current growth of available measurement data and resulting emphasis on data-driven modeling motivates algorithmic approaches for model discovery. A number of such approaches have been developed in recent years and have generated widespread interest, including the sparse regression problems, operator inference, physics-informed kriging, and DeepONets. After an overview of the current state of the art, this project can focus on either theoretical aspects related with some of the recently proposed strategies and their comparison, or their application to, e.g., a reduced representation of structural mechanics problems.

Deep learning-based reduced order models for uncertainty quantification in computational mechanics

Being able to solve differential problems rapidly, yet accurately, is a key task in order to handle both forward and inverse uncertainty quantification (UQ) problems in engineering. Thanks to the combined use of deep (e.g., feedforward, convolutional, autoencoder) neural networks and dimensionality reduction through proper orthogonal decomposition (POD, that is, principal component analysis), recently proposed deep learning-based reduced order models (POD-DL-ROMs, see **arXiv:2101.11845**) allow us to solve parametrized differential problems non-intrusively, in real-time. Hence, they are natural candidate surrogate models to enable the solution of UQ problems involving nonlinear parametrized PDEs such as, e.g., in computational mechanics. This project focuses on the use of POD-DL-ROMs in UQ, starting from their implementation in Tensorflow, and combining them with efficient sampling techniques.

*Iheart,Eu Erc Advanced Grant*

An Integrated Heart Model for the
simulation of the cardiac function.
The goal of the iHEART project is to construct, mathematically analyze, numerically approximate, computationally solve, and validate on clinically relevant cases a mathematically-based integrated heart model for the human cardiac function. The integrated model comprises several core cardiac models - electrophysiology, solid and fluid mechanics, microscopic cellular force generation, and valve dynamics - which are then coupled and finally embedded into the systemic and pulmonary blood circulations. It is a multiscale system of Partial Differential Equations and Ordinary Differential Equations featuring multiphysics interactions among the core models.