# Master theses

Students from Italian and foreign universities can develop their thesis project at MOX, in modelling, applied mathematics, numerical analysis and statistics.

#### Performance indicators for survival outcome

Advisor: Francesca Ieva    Contact the proponent if interested in this project.
Abstract:

Performance measures for institutions represent an important aspect concerning services quality. In the last years, there has been an increasing use of performance indicators in health care [1]. A performance indicator is a statistical measurement related to the quality of functioning of an institution. These measures concern different aspects and they must account for all indicators to have a summary outcome as plausible as possible. There is an ongoing debate about the best choice of indicator measures and their reliability. To establish which is the best performance indicator it is a difficult decision both for clinicians and statisticians.  The problem is how well a specific indicator reflects the quality of institution and how to draw conclusions from the estimates obtained by modeling the data. In order to quantify these results, in clinical literature rankings and league tables are usually created.

Performance indicators for hospitals could be for example proportion of complications, observed or expected mortality rate, proportion of patients still alive at a specific time point. When such indicators are built, appropriate statistical methodology to illustrate the presence of uncertainty in the presentation of results and the adjustment for case-mix is required. All individuals’ characteristics, known as case-mix, such as age, sex, diagnosis, stage of disease, therapy administered etc, are generally taken into account in statistical analysis. A fair comparison between centers is made after adjusting for case-mix [2-4].

Funnel plots [2] are well known tool used to compare institutions when the outcome is binary but little research has been performed for survival outcomes. Quaresma et al. [3] provide funnel plots as graphical tools designed to display performance indicators for cancer survival. To compare performance between institutions fixed or random effects models can be used.

The aim of this thesis is to provide performance indicators for survival outcomes to compare hospitals.

The motivating example comes from data about patients that underwent a surgery for oesophageal cancer in a Dutch hospital. The presence of about 55% of patients with unknown surgery date, which is the starting time for the event of interest, requires an algorithm to estimate this quantity. In this thesis an algorithm to impute missing values will be investigated. A simulations study will be performed to study the performance of method proposed.

1. Marshall C. and Spiegelhalter D.J., Reliability of league tables of in vitro fertil- ization clinics: retrospective analysis of live birth rates. British Medical Journal, 1998;316:1701-1705.
2. Spiegelhalter D.J., Funnel plots for comparing institutional performance. Statis- ticsin Medicine, 2005; 24:1185-1202.
3. Quaresma M., Funnel plots for population-based cancer survival: principles, methods and applications. Statistics in Medicine, 2014; 33: 1070-80.
4. D. Henneman, A. C. M. van Bommel, A. S. Snijders, R.A. A. E. Tollenaar, M.W.J.M. Wouters, M. Fiocco. Ranking­ and­ rankability­ of­ hospital­ postoperati­ve­ mortality­ rates­ in­ colorectal­ cancer­ surgery. Annals of Surgery 20 4 May;259(5):844-9
5. He Y., Normand S.-L. T., On the accuracy of classifying hospitals on their performance measures. Statistics in Medicine, 2014; 33:1081-1103.
6. Laird N. M. and Louis T. A., Empirical Bayes Ranking Methods. Journal of Educational Statistics, Spring 1989, 14: 29-46.

Note:

The thesis will be carried out jointly with Prof. Marta Fiocco (University of Leiden and Leiden University Medical Center).

Advanced kowledge of software R is required.

#### Carte di controllo multivariate per ottimizzazione di processi industriali

Advisor: Anna Maria Paganoni    Contact the proponent if interested in this project.
Abstract:

La tesi vuole rispondere ad una domanda di ricerca posta dalla ditta GEWISS che si occupa di stampa ad iniezione. Il problema riguarda lo studio di alcune variabili che entrano in gioco nel processo al fine di ottimizzare congiuntamente la produzione. Tale attività di tesi prevede una stretta sinergia lavorativa con tale azienda. La tesi si inserisce nella linea di ricerca su . Il lavoro, pensato per una persona, ha un contenuto modellistico medio, un contenuto teorico medio e un contenuto di programmazione elevato. Complessivamente si tratta di una tesi di media difficoltà. Si consiglia di consultare la seguente bibliografia essenziale: I requisiti richiesti al laureando sono: Corsi del percorso Applied Statistics

Note:

relatore Paganoni, A.M.

#### Applicazione di tecniche di Machine Learning per l'analisi di immagini in ambito radio oncomico

Advisor: Francesca Ieva    Contact the proponent if interested in this project.
Abstract:

Il progresso della radioterapia nella cura delle lesioni tumorali pone sfide importanti alla modellistica di supporto della prognosi medica. L'analisi delle immagini provenienti dalle strumentazioni radiologiche richiede lo sviluppo di opportuni modelli di previsione per personalizzare la terapia del paziente. La tesi si inserisce nella linea di ricerca su Health Analytics.

Note:

Sono richieste buone capacità di programmazione in R e/o Python. Competenze di statistica e statistica applicata.

#### Algebraic Dynamic Multilevel method with local time-stepping (ADM-LTS) for simulations of multiphase flow with an adaptive saturation intepolator

Advisor: Luca Formaggia    Contact the proponent if interested in this project.
Abstract:

Context: Simulation of multiphase flow in natural formations requires to deal with many difficulties deriving from the multi-scale (both in time and space) nature of the process. In fact, geological formations have very large length scales compared to those at which most physical and chemical interactions occur. Additionally, even at the so called Darcy scale, natural porous media have highly heterogeneous properties (e.g, permeability). To accurately capture the physics of interest very high resolution grids are required. However, the size of the domains make high resolution simulations impractical for field-scale applications. The Algebraic Dynamic Multilevel (ADM) method [1] was introduced to allow to employ a dynamically defined grid resolution to highly heterogeneous domains. The system of
equations is discretized on a high-resolution grid (referred to as fine-scale) and then mapped to coarser grid resolutions in those regions where a high-resolution is not required.
Mapping the unknowns across different resolutions is performed through sequences of restriction and prolongation (interpolation) operators.
In [2] an adaptive multilevel prolongation operator for saturation unknowns is considered. This approach allows for a better reconstruction of the saturation distribution behind the fast-moving
fronts, i.e., where the saturation changes are slow.

Objectives: We have surrently  implemented an Algebraic Dynamic Multilevel scheme with a mass conservative local time-stepping strategy (ADM-LTS) that employs an adaptive multilevel grid both in space
and in time. The method is able to use a fine grid resolution only at the location of the moving saturation fronts, with computational advantages.
The aim of the thesis is to study the adaptive multilevel prolongation operator and to integrate it in the ADM-LTS approach already implemented in a MATLAB research code, test it and validate on academic
test cases.

[1] M. Cusini, C. van Kruijsdijk, H. Hajibeygi, Algebraic dynamic multilevel (ADM) method for fully implicit simulations of multiphase flow in porous media, Journal of Computational Physics 314 (2016) 60 – 79.

[2] M. Cusini, H. Hajibeygi, Algebraic dynamic multilevel (ADM) method for simulations of multiphase flow with an adaptive saturation interpolator, in: ECMOR XVI-16th European Conference on the Mathematics of Oil Recovery, 2018

Prerequisite: Basic knowledge of numerical methods for partial differential equations of parabolic and hyperbolic type. Programming in MATLAB

Plan of work. Study the current literature on ADM/ADM-LTS schemes. Understand the current MATLAB code. Study how to implement the algebraic dynamic multilevel method. Implement it in the MATLAB code and run some tests, analysing the results in terms of accuracy and efficiency.

Main spervisor: Luca Formaggia

Support Team: Ludovica del Popolo Carcioppolo (PhD student, developer of the MATLAB code), Anna Scotti (Assistant Professor).

Note:

The thesis stems from a collaboration with the Prof H. Hajibetgi of University of Delft. It concerns the development of efficient schemes for underground flows. In particular schemes that couples both space and time adaptation. A prototype code (in Matlab) is already available that implements parts of the procedure. Possibility of spending some time in Delft may be discussed.

#### Finite volume methods on unstructured meshes for numerical weather prediction

Advisor: Luca Bonaventura    Contact the proponent if interested in this project.
Abstract:
Note:

Context: Finite volume methods have only recently been shown to be competitive for numerical weather prediction, see [1], where a fully non hydrostatic three dimensional model for all scales of atmospheric motion has been presented. This model has however mostly been tested on quasi-uniform meshes.

Objectives: The goal of the thesis is to prepare fully unstructured meshes with local refinement over complex orography for the IFS-FVM model using the gmsh [2] software and to test the IFS-FVM performance on these meshes. The thesis work is in the framework of the ESCAPE2 H2020 project

http://www.hpc-escape2.eu/

and will be carried out in direct contact with the  IFS-FVM developers at the European Center for Medium Range Weather Forecasts (ECMWF), Reading, UK.

Prerequisite: Basic knowledge of numerical methods for hyperbolic problems, good programming skills in C/C++ and possibly Fortran2003, interest in parallel computing.

Plan of work: Studying the existing IFS-FVM implementation and available meshes. Develop strategies for automatic mesh refinement over complex orography. Testing the alternative approaches and the IFS-FVM performance over different meshes.

Main supervisor: Prof. Luca Bonaventura

Support team: Dr. Tommaso Benacchio, ECMWF developers team

References

[1] Kühnlein, C., Deconinck, W., Klein, R., Malardel, S., Piotrowski, Z. P., Smolarkiewicz, P. K., ... & Wedi, N. P. (2019). FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS. Geoscientific Model Development, 12(2), 651-676.

[2] Geuzaine, C., & Remacle, J. F. (2009). Gmsh: A 3?D finite element mesh generator with built?in pre?and post?processing facilities. International journal for numerical methods in engineering, 79(11), 1309-1331.

#### Simulazione FEM di strutture in legno /FEM simulation of timber structures

Advisor: Anna Scotti    Contact the proponent if interested in this project.
Abstract:

Il lavoro di tesi proposto è in collaborazione con il Dipartimento ABC (Architettura, Ingegneria delle Costruzioni e ambiente costruito) del Politecnico di Milano e si propone di affrontare il problema della simulazione numeriche di strutture formate aste in legno. Lo scopo finale è l'ottimizzazione del progetto in varie condizioni di carico previste dalla normativa. Sebbene esistano strumenti per la simulazione di tali strutture con il metodo degli elementi finiti (ad esempio RFEM, RTIMBER) questi solver non sono integrati con tool di progettazione parametrica quali Grasshopper, per cui il processo iterativo di ottimizzazione della struttura risulta macchinoso e "manuale". Intendiamo quindi sviluppare un solver indipendente e interfacciabile con Grasshopper (linguaggio Python) che sia in grado, seppure in configurazioni semplificare, di calcolare lo stato di sforzo-deformazione e di verificare strutture ad aste (eg. Travi e pilastri) in legno data la geometria e la configurazione di carico. Anche se, in condizioni normali di progetto il comportamento del legno è lineare elastico questo materiale presenta una diversa normativa che non permette l'utilizzo dei tool parametrici esistenti atti al calcolo di strutture in metallo. Possibili approfondimenti sono quindi lo studio della dipendenza del comportamento reologico dalle condizioni ambientali e in particolare dall'umidità assorbita, dal tempo e dall'eventuale esposizione al fuoco.

Riferimenti:

Daniel Konopka , Clemens Gebhardt , Michael Kaliske - Numerical modelling of wooden structures  Journal of Cultural Heritage 27S (2017)

B. D’Amico, A. Kermani, H. Zhang, A. Pugnale, S. Colabella, S. Pone - Timber gridshells: Numerical simulation, design and construction of a full scale structure. Structures, (2015).

[ENG]

The thesis is in collaboration with the ABC Department of Politecnico  and is focused on the simulation of timber structures. The final goal is the optimization of the project in different loading conditions according to the requirements and regulations. Although some tools for the FEM simulations of such structures are already available (e.g. RFEM, RTIMBER) these solvers are not integrated with parametric design tools such as  Grasshopper, and thus at the moment the iterative optimization process is manual and cumbersome. We plan to develop an independent solver that is compatible with Grasshopper (thus in Python) and is able to compute the stress and deformation state of timber beams/pillars structures, and to verify them given the geometry and the loading, even if, in the beginning, in simplified situations. Even if, in normal operating conditions timber behaves as linear elastic this material is subject to a different regulation that prevents us from using the simulation tools designed for metal structures. Possible developments of this work are thus the study of the dependence of the rheology in environmental conditions and in particular moisture sorption, on time and possibly on the exposure to fire.

References:

Daniel Konopka , Clemens Gebhardt , Michael Kaliske - Numerical modelling of wooden structures  Journal of Cultural Heritage 27S (2017)

B. D’Amico, A. Kermani, H. Zhang, A. Pugnale, S. Colabella, S. Pone - Timber gridshells: Numerical simulation, design and construction of a full scale structure. Structures, (2015).

Note:

In collaborazione con il Dipartimento ABC, dove un tesista è già operativo sul progetto.

#### Scenari di lungo termine per la modellizzazione dei fabbisogni di bilanciamento del sistema elettrico

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

Nell’ambito di una collaborazione con il Dipartimento di Energia, la tesi affronta il tema dello sviluppo di un modello dei mercati e del sistema elettrico Italiano (anche in relazione a quello Europeo) che possa fornire scenari di lungo termine sulla quantificazione dei fabbisogni di energia per il bilanciamento del sistema elettrico. In particolare, sarà necessario modellare i mercati elettrici in Italia, analizzando quali sono i fattori che influenzano maggiormente la richiesta di energia per il bilanciamento del sistema elettrico in tempo reale. A partire dal modello costruito, si potranno definire diversi scenari di lungo termine in corrispondenza di scelte d’investimento differenti attuate sia dal comparto pubblico che da quello privato.
Visti gli obiettivi nazionali ed europei legati alla sostenibilità ambientale ed alle energie rinnovabili, tale argomento risulta di fondamentale importanza ed interesse sia per gli attori di mercato sia per gli enti istituzionali e governativi che gestiscono il sistema elettrico ed energetico nazionale.
Il database di riferimento, contenente i dati grezzi su cui lavorare, risulta essere molto ricco e comprenderà sia i dati pubblici di mercato ottenibili dal sito mercatoelettrico.org sia altri dati ritenuti rilevanti.
La tesi verrà svolta in stretta collaborazione con il Dipartimento di Energia.

Note:

Co-relatore del Dipartimento di Energia del Politecnico di Milano: Ing. Filippo Bovera

#### Health Analytics for Myelodisplastic Syndromes

Advisor: Francesca Ieva    Contact the proponent if interested in this project.
Abstract:

Il contesto clinico è quello di alcuni tumori del sangue che si chiamano sindromi mielodisplastiche. Si tratta di leucemie croniche rare, che riducono drasticamente l’aspettativa di vita dei pazienti, e per i quali l’unica terapia curativa è il trapianto di midollo. Purtroppo il trapianto fallisce in una percentuale elevata di casi o per recidiva della malattia o per tossicità della procedura di trapianto stessa. Circa 10 anni fa sono cominciati studi per definire le mutazioni geniche ricorrenti alla base della malattia. Le mutazioni sono importanti per predire la prognosi dei pazienti e anche per definire la probabilità di successo del trapianto.

La/le tesi si focalizzerà/anno su:

1) Definire dei modelli predittivi innovativi, che comprendano anche le informazioni genomiche per predire la probabilità di successo del trapianto nel singolo paziente e quindi selezionare in modo ottimale i candidati a questa procedura.

2) Definire nel paziente candidato il momento ottimale (rispetto alla storia naturale della malattia) in cui eseguire la procedura di trapianto. Infatti la malattia ha diversi stati, e soprattutto per i pazienti diagnosticati in fase iniziale, puo’ passare molto tempo prima che la malattia intacchi lo stato di salute della persona. In questi soggetti, eseguire un trapianto subito al momento della diagnosi può risultare sconveniente, perché sarebbero sottoposti ai rischi del trapianto in una fase di malattia in cui l’impatto di salute è invece basso (rapporto rischi/beneficio sfavorevole)

Note:

Da questa proposta può nascere più di un progetto di tesi. La tesi si svolgerebbe su un progetto di collaborazione con Humanitas.

#### Algoritmi e modelli statistici per lo studio del Mercato per il Servizio di Dispacciamento

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

Nell’ambito di una collaborazione con il Dipartimento di Energia, la tesi affronta il tema dello sviluppo di algoritmi statistici in grado di modellizzare efficacemente le dinamiche di mercato attuali e di breve termine legate al dispacciamento elettrico, con particolare riferimento alla definizione, clusterizzazione e caratterizzazione delle condizioni al contorno che ne influenzano il funzionamento. Visti gli obiettivi nazionali ed europei legati alla sostenibilità ambientale ed alle energie rinnovabili, tale argomento risulta di fondamentale importanza ed interesse sia per gli attori di mercato sia per gli enti istituzionali e governativi che gestiscono il sistema elettrico ed energetico nazionale.
Il database di riferimento, contenente i dati grezzi su cui lavorare, risulta essere molto ricco e comprenderà sia i dati pubblici di mercato ottenibili dal sito mercatoelettrico.org sia altri dati ritenuti rilevanti.
La tesi verrà svolta in stretta collaborazione con il Dipartimento di Energia, con l’eventuale possibilità di tradurre in un componente hardware, e verificare su impianti reali, l’algoritmo sviluppato durante il lavoro di tesi o successivamente alla sua conclusione.

Note:

Co-relatore del Dipartimento di Energia del Politecnico di Milano: Ing. Filippo Bovera

#### Simulation of wave propagation in unbounded domains

Advisor: Tommaso Benacchio    Contact the proponent if interested in this project.
Abstract:

The project aims to devise and implement numerical discretizations of hyperbolic systems of geophysical fluid dynamics (shallow water equations, compressible Euler equations) on multidimensional semi-infinite strips, building on existing models for the one-dimensional case developed by T. Benacchio and L. Bonaventura. Continuous and discontinuous finite element discretizations will be used in the finite directions and Laguerre-based spectral methods will be used in the unbounded direction. Subject to good performance on standalone tests, the model will be coupled to a finite-element based discretization on a finite domain. The coupled setup will be used to perform wave propagation experiments, including tests in thermally stratified environments.
As one of several applications, the resulting code will supply efficient absorbing boundary conditions at model tops of state-of-the-art numerical weather prediction systems. The project is in collaboration with G. Tumolo (European Centre for Medium-Range Weather Forecasts, UK).

References:

Benacchio, T., and L. Bonaventura, 2013: Absorbing boundary conditions: a spectral collocations approach. International Journal of Numerical Methods in Fluids, 72, 913-936, doi: 10.1002/fld.3768.

Benacchio, T. and L. Bonaventura, 2019: An extension of DG methods for hyperbolic problems to one-dimensional semi-infinite domains. Applied Mathematics and Computation, 350, 266-282, doi: 10.1016/j.amc.2018.12.057.

Tumolo, G. and L. Bonaventura, 2015: A semi-implicit, semi-Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction. Quarterly Journal of the Royal Meteorological Society, 141, 2582-2601, doi: 10.1002/qj.2544.

Note:

Prerequisites: ANEDP2

#### Efficient and scalable solvers for numerical weather prediction

Advisor: Tommaso Benacchio    Contact the proponent if interested in this project.
Abstract:

Timely and trustworthy weather forecasts rely on accurate and efficient underlying numerical methods, and numerical weather prediction simulations are the ideal testbed for high-performance computing hardware towards the exascale. The project aims at exploring and extending numerical algorithms used in state-of-the-art models of atmospheric dynamics by:

1. On existing code bases, performing efficiency and scalability studies with linear solvers applied to the solution of simplified models of atmospheric flow;
2. Based on the development at point 1., applying the techniques to the implementation of solvers within semi-implicit discretizations of more complex equation sets and analyze their performance on benchmarks at different spatial and temporal scales.

The programming activity will be carried out using recently developed mini-apps ('dwarfs') produced by the EU project ESCAPE, and will be strongly connected to the current activities of the ESCAPE-2 EU project at MOX. Knowledge of, or willingness to learn, Fortran and shell scripting would be required for the project.

The project includes a partially funded research stay at the European Centre for Medium-Range Weather Forecasts in Reading, UK. This will give the opportunity to interact with scientists in the Numerical Methods team and to present the results of the work in a Research Seminar at the Centre.

References:

ESCAPE-2 project: www.hpc-escape2.eu

Melvin, T., T. Benacchio, B. Shipway, N. Wood, J. Thuburn, and C. J. Cotter, 2018: A mixed finite-element, finite-volume, semi-implicit discretisation for atmospheric dynamics: Cartesian geometry. Q. J. Roy. Meteor. Soc., in press, doi: https://doi.org/10.1002/qj.3501.

Mueller, A., et al., 2019: The ESCAPE project: Energy-efficient Scalable Algorithms for Weather Prediction at Exascale, Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2018-304, in review, 2019.

Tumolo, G. and L. Bonaventura, 2015: A semi-implicit, semi-Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction. Quarterly Journal of the Royal Meteorological Society, 141, 2582-2601, doi: 10.1002/qj.2544.

Note:

Prerequisites: ANEDP2, APSC

#### Numerical models for fault reactivation based on Nitsche's formulation

Advisor: Luca Formaggia    Contact the proponent if interested in this project.
Abstract:

The exploitation of the underground because of oil/gas extraction, CO2 sequestration, geothermal energy storage or other human activities causes and alteration of the underground flow and may reactivate a fault, causing it to slip and generate seismic activity. To estimate the risk it is necessary to consider a coupled problem involving flow in faulted media, poroelasticity and frictional contact. It gives rise to a complex non-linear equations involving inequality constraints. An interesting approach consider the fault as an immersed interface and suitable conditions to represent the frictional contact along the fault. Numerically, the problem is solved resorting to a Nitsche formulation and extended finite elements. A prototype code has been developed and the student is requested to try different possible formulations. An original approach is to reinterpret the probloble as a non-linear control problem, another possibility is to use iterative techniques for a special formulation of the frictional contact problem along the fault. The thesis may be carried out by one or two persons. In the case of two students, it would be optima to have one students more oriented to scientific programming and the other to the theoretical analysis of the scheme. La tesi si inserisce nella linea di ricerca su Metodi per equazioni alle derivate parziali. Il lavoro, pensato per una persona, ha un contenuto modellistico elevato, un contenuto teorico elevato e un contenuto di programmazione elevato.

Complessivamente si tratta di una tesi di elevata difficoltà. Si consiglia di consultare la seguente bibliografia essenziale: Quarteroni,A., MODELLISTICA NUMERICA per PROBLEMI DIFFERENZIALI, Springer-VerlagC. Annavarrapu et al. A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: Single interface, 2014, https://doi.org/10.1007/978-3-319-71431-8 Chouly F. et al, An Overview of Recent Results on Nitsche's Method for Contact Problems, 2018, https://doi.org/10.1007/978-3-319-71431-8 Chouly et al, A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis, 2013, https://doi.org/10.1137/12088344X J. Both et al, Robust fixed stress splitting for Biot's equations in heterogeneous media, 2016, https://doi.org/10.1016/j.aml.2016.12.019 Notes provided by the supervisors I requisiti richiesti al laureando sono: C++ programming skill, good knowledge of numerical methods for PDEs. Willingness to learn advanced numerical methods. Interest in modelling complex non-linear phenomena.

Note:

relatore Formaggia, L, secondo relatore Scotti, A

#### Functional data over complex volumetric domains, with applications to neuroimaging

Advisor: Laura maria Sangalli    Contact the proponent if interested in this project.
Abstract:

This thesis aims at developing a rich class of models for the analysis of functional data observed over volumetric domains with non-trivial geometries. These methods might have a huge impact in neuroimaging applications, offering for the very first time techniques able to efficiently comply with the complex shape of the brain.

Note:

#### Data on manifolds

Advisor: Laura maria Sangalli    Contact the proponent if interested in this project.
Abstract:

The student will develop innovative methods for the analysis of data distributed over two-dimensional Riemannian manifolds. Such data are common in varied contexts. In the neurosciences, for instance, it is of great interest to study signals associated to neuronal activity over the cerebral cortex, a highly convoluted thin sheet of neural tissue that constitutes the outermost part of the brain. In the geosciences, data are often collected over surface domains such as the full globe or other regions with complex orography. In the engineering, especially in the automotive, naval, aircraft and space sectors, it is crucial for design optimization to analyze quantities of interest over the surface of the designed 3D object (e.g, to analyze air pressure over a shuttle winglet).

Note:

#### Forward Uncertainty Quantification for Dynamical Systems

Advisor: Andrea Manzoni    Contact the proponent if interested in this project.
Abstract:

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).

Note:

#### Partially observed functional data

Advisor: Laura maria Sangalli    Contact the proponent if interested in this project.
Abstract:

This thesis aims at developing innovative methods for the analysis of partially observed functional data. In many applicative domains, it is in fact common to encounter sets of functional data where some portion of the functional datum is missing for some statistical units. This unfortunately invalidates most of the existing techniques for functional data analysis, calling for the development of novel methods.

Note:

#### Advanced statistical and numerical methods for high-dimensional functional data

Advisor: Laura maria Sangalli    Contact the proponent if interested in this project.
Abstract:

Multiple theses are available concerning the development of innovative methods for the analysis of high-dimensional functional data, interfacing advanced techniques from statistics and from numerical analysis. The new methods will be applied to complex problems in the life sciences, environmental sciences, or engineering.

Note:

#### Statistics for Neurosciences: new methods for the analysis of neuroimaging data

Advisor: Laura maria Sangalli    Contact the proponent if interested in this project.
Abstract:

The student will develop new methods for the analysis of high-dimensional and complex signals arising from neuroimaging modalities, such as functional magnetic resonance imaging or magnetoencephalography. Differently from the techniques currently available in the literature, these new methods will be able to efficiently comply with the complex anatomy of the brain, which highly influences the signals under study. This model feature may lead to breakthrough advances in the neurosciences.

Note:

#### Statistical and Machine learning methods for predicting high school students dropout

Advisor: Chiara Masci    Contact the proponent if interested in this project.
Abstract:

The proposed thesis is part of a research project called "Piacenza Orientata" that sees the collaboration of the Department of Mathematics and the Department of Management of Politencico di Milano. The aim of the work is to analyze data about high school students in Piacenza and develop statistical models (also including machine learning techniques) to predict students dropout at the first year of high school, observing collateral information of students and their previous career.

Note:

#### Simulazione di fluidi a superfie libera con reologia complessa

Advisor: Luca Formaggia    Contact the proponent if interested in this project.
Abstract:

Scopo del lavoro di tesi è lo studio di metodi numerici per il tracciamento dello spostamento della superficie libera di un fluido [1] e la loro
implementazione in un codice di calcolo parallelo basato su griglie cartesiane con raffinamento gerarchico adattivo [2, 3].

Il contesto applicativo è quello della valutazione del rischio connesso ad eventi catastrofici ed in particolare alla simulazione di frane
e colate laviche [4,5,6].

Il progetto si svolge nell'ambito di una collaborazione con l'Agenzia Spaziale Italiana volta a sviluppare metodi numerici e statistici per la valutazione dei rischi naturali che integrino modelli fisici e dati relativi ad osservazioni satellitari [7].

Bibliografia :

[1] Viljami Laurmaa, Marco Picasso and Gilles Steiner, "An octree-based adaptive semi-Lagrangian VOF approach for simulating the displacement of free surfaces." Computers & Fluids, Volume 131, 5 June 2016, Pages 190-204

[2] Pasquale Africa, Simona Perotto and Carlo de Falco"Scalable Recovery-Based Adaptation on Quadtree Meshes" In preparation

[3] Pasquale Africa, "Scalable adaptive simulation of organic thin-film transistors" Tesi di Dottorato in MODELLI E METODI MATEMATICI PER L'INGEGNERIA, 2019

[4] M.Cremonesi, F.Ferri and U.Perego. "A basal slip model for Lagrangian finite element simulations of 3D landslides." International Journal for Numerical and Analytical Methods in Geomechanics, 41(1), 2017

[5] Andrew J. Harris S. Rowland, "FLOWGO: a kinematic thermo-rheological model for lava flowing in a channel" Bulletin of Volcanology, May 2001, Volume 63, Issue 1, pp 20-44

[6] Ovarlez, Guillaume, Hormozi, Sarah (Eds.) "Lectures on Visco-Plastic Fluid Mechanics" Springer, 2019

[7] Pasquale C. Africa, Mara S. Bernardi et. al. "Use of Earth observation satellite data for monitoring and forecasting natural hazards"
In preparation

Note:

La tesi si inserisce all'interno di un progetto di ricerca con l'Agenzia Spaziale Italiana, volto a sviluppare metodi numerici e statistici per la valutazione dei rischi naturali che integrino modelli fisici e dati relativi ad osservazioni satellitari. Sara seguita dai proff.  Luca Formaggia e Carlo de Falco.

#### Metodi multi-level Monte Carlo Discontinuous Galerkin per problemi di propagazione di onde acustiche in mezzi eterogenei.

Advisor: Paola francesca Antonietti    Contact the proponent if interested in this project.
Abstract:
```La tesi riguarda lo sviluppo, l'analisi e l'implementazione di un algoritmo Monte Carlo multi-livello per il calcolo delle statistiche di quantità stocastiche di interesse descritte per problemi di propagazione di onde con parametri stocastici. La sequenza di discretizzazioni multilivello e' basata su un metodo Discontinuous Galerkin di ordine variabile per la discretizzazione di un problema di propagazione di onde acustiche in mezzi eterogenei.

La proposta di tesi e' in co-supervisione con il Dr. Andrea Manzoni.```

Rif. Bibliografici:

M. Motamed and D. Appelo. A Multi-Order Discontinuous Galerkin Monte Carlo Method for Hyperbolic Problems with Stochastic parameters. SIAM J. Numerical Analysis, vol. 56, pp. 448-468, 2018.

Note:

#### Una semplice implementazione delle condizioni al bordo PML per problemi di propagazione di onde in domini elasto-acoustici

Advisor: Ilario Mazzieri    Contact the proponent if interested in this project.
Abstract:
```La tesi riguarda l'analisi e l'implementazione delle condizioni al bordo Nearly Perfect Matched Layer (NPML) per problemi differenziali iperbolici
del secondo ordine in domini elasto-acustici.

Rif. bibliografici:
M. Zhuang, Q. Zhan, J. Zhou, Z. Guo, N. Liu, Q. H. Liu, A simple implementation of PML for second-order elastic wave equations, Computer Physics Communications, Volume 246, 2020```

Note:

#### ADVANCED AND ARTIFICIAL INTELLIGENCE TECHNIQUES TO MITIGATE LINEAR AND NON-LINEAR IMPERFECTIONS IN FUTURE CIRCULAR COLLIDERS

Advisor: Luca Bonaventura    Contact the proponent if interested in this project.
Abstract:

The thesis will focus on the numerical modelling of particle tracking in circular particle colliders planned for future deployment at CERN. This thesis will focus on the optimization of the hadron option of the future circular collider against linear and non-linear imperfections (i.e. magnets alignments and their field quality). A key point of the thesis will be the comparison of current advanced correction schemes to techniques based on machine learning. The thesis will be tutored in collaboration with Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA) – France and could entail a stage at CEA (located a Saclay close to Paris) that could be supported financially by CEA (application for funding is pending).

Note:

Full thesis description available on request

#### Wasserstein metrics for functional data analysis

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

Wasserstein metrics have appealing properties and induce interesting geodesic structures on the space of probability measures. This project explores the potential of such metrics for the statistical analysis of functional data.

The most immediate approach is built on operators mapping sets of functions in spaces of densities. The key property that must be asserted for such operators is continuity with respect to some functional metric. One can then use statistical methods developed for Wasserstein Spaces (in particular for 1-D distributions) to carry out analysis of functional datasets.

Note:

In collaborazione con il Dott. Matteo Pegoraro

#### Statistical post-processing of ensemble methods for prediction of spatially dependent data

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

Ensemble methods for regression or classification, like random forests or boosting, are becoming the general tool of choice in statistical learning for tackling prediction problems characterized by large amount of training data. Post-processors of ensemble predictors based on Lasso have been proposed by Friedman and Popescu (2008) [ Friedman J. and Popescu B. (2005), Predictive Learning via Rule Ensembles. arXiv:0811.1679]. This project aims at developing post-processors of ensemble methods apt to the prediction of spatially dependent data. The research will move from the analysis of  the RDD-UK ensemble method recently introduced in Menafoglio et al. (2018) [A. Menafoglio, G. Gaetani, P. Secchi (2018), Random domain decompositions for object-oriented Kriging over complex domains, Stochastic Environmental Research and Risk Assessment, 32(12), 3421-3437] for Kriging spatially dependent object data.

Note:

In collaborazione con il dott. Riccardo Scimone

#### Studio e implementazione di basi polinomiali ortogonali su elementi poligonali o poliedrici per la discretizzazione di PDE con elementi virtuali

Advisor: Alessio Fumagalli    Contact the proponent if interested in this project.
Abstract:

Quando si considerano mesh con elementi con grande aspect ratio o lati con dimensioni molto diverse, l'uso delle basi monomiali per l'implementazione di elementi VEM risulta mostrare instabilità dovute a problemi di condizionamento numerico. In questi casi sono necessarie basi polinomiali alternative che mostrano buone proprietà di robustezza. La proposta di tesi riguarda lo sviluppo e l'implementazione di tali basi alternative.

Note:

L'attivita' di tesi e' in collaborazione con il Politecnico di Torino. Conoscenze richieste: buona conoscenza di metodi FEM (teoria e implementazione)

#### Recurrent patterns of mobility on the metro system of Milan.

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

The aim of the thesis is to identify recurrent patterns in the passengers' daily access to stations (and subway sections) under different scenarios of demand and offer, to extract useful insights that can help the transport company to best handle the service (e.g. minimizing crowding situations). In detail, the student will use and apply clustering and bi-clustering techniques for high dimensional data. The thesis will use and possibly expand bi-clustering techniques developed in Galvani, M. et al. (2020)[Galvani, M.; Torti, A.; Menafoglio, A.; Vantini S. 2020 (FunCC: a new bi-clustering algorithm for functional data with misalignment

Note:

Joint supervision with Ing. Agostino Torti

#### Mobility flows on the metro system of Milano

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

The aim of the thesis is to explore the features of the subway network under different scenarios of demand and offer, to extract useful insights that can help the transport company to best handle the service (e.g. minimizing crowding situations).  In detail, the student will use and apply tools from network analysis performing macro/ meso/micro scale analyses [M.E.J. Newman (2010): Networks: an Introduction, Oxford University press]

Note:

Joint supervision with Ing. Agostino Torti

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

Advisor: Andrea Manzoni    Contact the proponent if interested in this project.
Abstract:

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:2102.13403, 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.

Note:

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

Advisor: Andrea Manzoni    Contact the proponent if interested in this project.
Abstract:

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.

Note:

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

Advisor: Andrea Manzoni    Contact the proponent if interested in this project.
Abstract:

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.

Note:

#### Joint frailty modelling of time-to-event data to elicit the evolution pathway of events: a generalised linear mixed model approach.

Advisor: Francesca Ieva    Contact the proponent if interested in this project.
Abstract:

La tesi ha risvolti metodologici e applicativi (ambito clinico ed epidemiologico). E' necessario un solido background in statistica applicata e una buona conoscenza di almeno uno dei seguenti software: R, Python.

Note:

La proposta rientra nelle attività di Health Analytics sviluppate al MOX.
Co-supervisors: dott.ssa Marta Spreafico; dott.ssa Chiara Masci

#### Modelli Markoviani e metodi computazionali per lo sviluppo di un simulatore del gioco della pallavolo.

Advisor: Piercesare Secchi    Contact the proponent if interested in this project.
Abstract:

Il lavoro di tesi svilupperà modelli markoviani e metodi computazionali per lo sviluppo di un simulatore del gioco della pallavolo, costruito a partire dall’analisi di dati che descrivono il gioco reale. In questo contesto, le possibili attività per lo sviluppo della tesi sono molteplici: sia natura computazionale (parallelizzazione del calcolo e riduzione dei tempi computazionali) che di natura inferenziale per l’analisi di incertezza relativa ai parametri che governano il modello di gioco, e per la robustezza e stabilità del modello di simulazione. Il simulatore si propone come strumento per il supporto alle decisioni nella fase di preparazione strategica pre-gara di squadre professionistiche. La tesi prevede uno stage in Math&Sport: https://www.mathandsport.com/it/home-2/

Note:

In collaborazione con l'Ing. Di Maulo di Math&Sport

#### Fattori di rischio cardiovascolari in soggetti con infezione da HIV

Advisor: Francesca Ieva    Contact the proponent if interested in this project.
Abstract:

Sviluppo di algoritmi di algoritmi di Machine Learning per la valutazione dei fattori predittivi l’insorgenza di eventi cardiovascolari in soggetti con infezione da HIV con Follow Up di 10 anni.

Note:

Progetto di ricerca in collaborazione con il Dipartimento di Infettivologia dell’Università Vita-Salute – San Raffaele.

Richiesta expertise di programmazione in R o Python.

Partenza Marzo 2021.

#### Application of multifidelity functional surrogate approaches to uncertainty quantification in subsurface modelling

Advisor: Alessandra Menafoglio    Contact the proponent if interested in this project.
Abstract:

Obiettivo:

L’obiettivo della tesi consiste nell’applicare la metodologia multifidelity functional surrogate modeling in ambito subsurface/reservoir per ottenere la quantificazione dell’incertezza delle previsioni basate su modello.  Si vuole inoltre confrontare il metodo con le tecniche più tradizionali di surrogate modeling utilizzate attualmente su un caso di complessità realistica.

Proposta possibili attività:

Le attività potrebbero organizzarsi secondo lo schema seguente:

1. Revisione dello stato dell’arte basata sui lavori più recenti sviluppati sul tema in particolare facendo riferimento alle pubblicazioni [2] e [3] nella sezione references;
2. Familiarizzazione con
1. il prototipo di multifidelity surrogate modelling sviluppato in [2] che comprende sia l’approccio di Cokriging funzionale, sia alcune semplici tecniche di upscaling più comunemente utilizzate in ambito subsurface/reservoir ;
2. la simulazione multifase di fluidi in mezzo poroso utilizzando inizialmente il tool open source OPM Flow;
3. Gestione dell’incertezza su modello realistico attraverso opportuno campionamento e realizzazioni multiple utilizzando un simulatore industriale su sistemi HPC basati su GPU;
4. Quantificazione dell’incertezza sia con approccio functional-multifidelity sia con metodi tradizionali e confronto;
5. Stesura report con la discussione del confronto relativo al punto 4 e documentazione del codice prototipo;

References

1. Aliyev, E. and Durlofsky, L.J. “Multilevel field development optimization under uncertainty using a sequence of upscaled models. Mathematical Geosciences, 49(3), 307–339. 2017.
2. M. Bezzegato: “Multifidelity surrogate modeling in reservoir simulation: a functional cokriging approach to uncertainty quantification and prediction”, M. Sc. in Mathematical Engineering Thesis, 2019;
3. Grujic, O., Menafoglio, A., Yang, G. and Caers, J. “Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation”. Stochastic Environmental Research and Risk Assessment, 32(7), 1955–1971. 2018.
4. Kostakis, F. F., Mallison, B. T., and Durlofsky, L. J.. "Multifidelity Framework For Uncertainty Quantification With Multiple Quantities Of Interest." ECMOR XVI-16th European Conference on the Mathematics of Oil Recovery. 2018.
5. Thenon, A., Gervais, V.,  and Le Ravalec, M.. "Multi-fidelity meta-modeling for reservoir engineering-application to history matching." Computational Geosciences 20.6 (2016): 1231-1250.
6. Thenon, A., Gervais V., Le Ravalec, M. "Multi-fidelity Proxy Models for Reservoir Engineering." ECMOR XV-15th European Conference on the Mathematics of Oil Recovery. 2016.

Note:

Il lavoro di tesi prevede lo svolgimento di un periodo di stage presso Eni della durata di 3 mesi, da svolgersi nel corso del 2021 (autunno 2021). Il lavoro sarà svolto in collaborazione con i ricercatori di Eni e con la co-supervisione del prof. A. Manzoni.

#### From coronavirus infections to neurodegenerative diseases: Shape transitions in axons

Advisor: Davide Riccobelli    Contact the proponent if interested in this project.
Abstract:

Many pathologies, ranging from coronavirus infections to neurodegenerative diseases, can alter the physiological morphology of axons, which are slender protusions of neurons which transmit electro-chemical 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 in-vitro 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.