Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation

Hess MW, Quaini A, Rozza G. A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation. 2022 .

Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics

Hess MW, Quaini A, Rozza G. Data-Driven Enhanced Model Reduction for Bifurcating Models in Computational Fluid Dynamics. 2022 .

Full Order Model and Reduced Order Model Consistency for Evolve-Filter-Relax Regularization

Read more about Full Order Model and Reduced Order Model Consistency for Evolve-Filter-Relax Regularization

Deep Learning approximation of diffeomorphisms via linear-control systems

Read more about Deep Learning approximation of diffeomorphisms via linear-control systems

Optimal design of planar shapes with active materials

Read more about Optimal design of planar shapes with active materials

Introduction to sub-Riemannian geometry

The aim of this course is to provide an introduction to the geometry of sub-Riemannian manifolds, and to illustrate some research directions in this domain.

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