Altre Aree 
Enrico Zio  Dipartimento di Energia 
Prognostics and Health Management (PHM)


Analisi Numerica 
Paola Francesca Antonietti  Dipartimento di Matematica 
Polygonal Discontinuous Galeking methods enhanced by Machine Learning techniques
Tesi in con supervisione con S. Bonetti.

Descrizione
The interaction between the world of numerical analysis and machine learning (ML) algorithms is becoming more and more important day by day, seeing ML algorithms as a means to improve the convergence of classical (and even not classical) numerical methods. This thesis aims to combine the techniques of Polytopal Discontinuous Galerkin (PolyDG) methods with new machine learning techniques.
The PolyDG methods for the spatial discretization of PDEs are numerical methods of great interest as they can guarantee a high level of geometric flexibility and arbitraryorder accuracy. Specifically, the final goal of the work is to develop and implement a machine learning algorithm that, given a polygonal or polyhedral mesh as input, returns optimal penalty parameters for PolyDG methods as output, so that we can reach the optimal rate of convergence. The resulting algorithm will be tested initially on standard problems and then on more complex problems with geophysical applications, such as CO2 storage or geothermal energy extraction.
References:
 P.F. Antonietti, M. Caldana, L. Dede’. Accelerating Algebraic Multigrid Methods via Artificial Neural Networks. arXiv.org: https://arxiv.org/abs/2111.01629
 P. F. Antonietti, C. Facciolà, P. Houston, I. Mazzieri, G. Pennesi, and M. Verani. High–orderDiscontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: SeismicWave Propagation and Fractured Reservoir Simulations, pp. 159–225. Springer International Publishing, Cham, 2021. ISBN 9783030693633. doi: 10.1007/9783030693633_5
 A. Cangiani, Z. Dong, E. H. Georgoulis, and P. Houston. hpversion discontinuous Galerkinmethods on polytopic meshes. Springer Briefs in Mathematics. Springer International Publishing, 2017

Analisi Numerica 
Paola Francesca Antonietti  Dipartimento di Matematica 
Discontinuous Galerkin methods for thermoporoelastic equations
Tesi in cosupervision con M. Botti e S. Bonetti

Descrizione
In many applications involving geophysical phenomena, including environmental sustainability problems such as geothermal energy production and CO2 storage, it is of crucial importance to study the responses of the subsurface to the injection of a fluid into it. To study this problem, thermoporoelasticity models have been introduced: models for fully coupled multiphysics problems. The thesis aims to perform numerical simulations for the thermoporoelastic equations, and the final goal is to forecast the effects of injecting a fluid in the subsoil in a realistic scenario of geothermal energy extraction; the analysis will focus on the resulting waves propagation phenomena. Polytopal Discontinuous Galerkin (PolyDG) methods will be employed for the semidiscrete approximation of the corresponding differential system because of their high geometric flexibility and arbitrary order accuracy.
References:
 P.F. Antonietti, S. Bonetti, M. Botti. Polytopal discontinuous Galerkin discretization methods for fullycoupled thermoporoelasticity. In preparation, 2022
 J. M. Carcione, F. Cavallini, E. Wang, J. Ba, and L.Y. Fu. Physics and simulation of wave propagation in linear thermoporoelastic media. Journal of Geophysical Research : Solid Earth, 124(8): 8147–8166, 2019. doi: https://doi.org/10.1029/2019JB0178

Analisi Numerica 
Paola Francesca Antonietti  Dipartimento di Matematica 
Discontinuous Galerkin methods for magnetoquasistatic Maxwell equations

Descrizione
The goal of the thesis is to perform numerical simulations for the magnetoquasistatic Maxwell equations. The final goal is to forecast the effects of subsurface telluric electric currents, concentrated in the Earth’s interior, on the direction and on the intensity of the geomagnetic field measured at the surface, especially in the ULF band of radiofrequencies. Discontinuous Galerkin methods will be employed for the semidiscrete approximation of the corresponding differntial system that appears in models of classical electrodynamics in heterogeneous media.

Fisica Matematica 
Davide Riccobelli  Dipartimento di Matematica 
From coronavirus infections to neurodegenerative diseases: Shape transitions in axons

Descrizione
Many pathologies, ranging from coronavirus infections to neurodegenerative diseases, can alter the physiological morphology of axons, which are slender protusions of neurons which transmit electrochemical signals. The aim of this thesis is to model the dynamical changes of shape induced by these diseases on neuronal cells and to compare them with invitro experiments performed on human axons. According to the preferences of the student the work can be more devoted to theoretical aspects and to the development of innovative models or to the design of robust numerical schemes.
For further information, please contact me by email.

Altre Aree 
Enrico Zio  Dipartimento di Energia 
Reliability, Safety and Risk


Altre Aree 
Alberto Zasso  Dipartimento di Meccanica 
Statistical analysis of peak pressures on building façades


Altre Aree 
Domenico Brunetto  Dipartimento di Matematica 
Mathematical models for learning

Descrizione
Such work aims to develop mathematical models within the context of social interaction, in particular during the students' learning process. Resorting the main results in the field of opinion dynamics and social networks, we develop a tool that allows instructors at monitoring the learning dynamics in a controlled learning environment. The main challenge is to equip the mathematical model with social ones, such as affect views. The dissertation can be either theoretical or experimental work.

