Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1251 prodotti
-
20/2023 - 24/02/2023
Ciaramella, G.; Nobile, F.; Vanzan, T.
A multigrid method for PDE-constrained optimization with uncertain inputs | Abstract | | We present a multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty. The algorithm is based on a collective smoother that at each iteration sweeps over the nodes of the computational mesh, and solves a reduced saddle-point system whose size depends on the number N of samples used to discretized the probability space. We show that this reduced system can be solved with optimal O(N) complexity. We test the multigrid method on three problems: a linear-quadratic problem for which the multigrid method is used to solve directly the linear optimality system; a nonsmooth problem with box constraints and L 1 -norm penalization on the control, in which the multigrid scheme is used within a semismooth Newton iteration; a risk-adverse problem with the smoothed CVaR risk measure where the multigrid method is called within a preconditioned Newton iteration. In all cases, the multigrid algorithm exhibits very good performances and robustness with respect to all parameters of interest. |
-
19/2023 - 24/02/2023
Marcinno', F.; Vergara, C.; Giovannacci, L.; Quarteroni, A.; Prouse, G.
Computational fluid-structure interaction analysis of the end-to-side radio-cephalic arteriovenous fistula | Abstract | | In the current work, we present a fluid-structure interaction study of the end-tosideradio-
cephalic arteriovenous fistula. The core of the work consists in simulating
different arteriovenous fistula configurations obtained by virtually varying the
anastomosis angle, i.e. the angle between the end of the cephalic vein and the side of
the radial artery.The mesh used to solve the structural problem takes into account the
different thickness and Young's modulus of the vessel walls. In particular, since the aim
of the work is to understand the blood dynamics in the very first days after the surgical
intervention, the radial artery is considered stiffer and thicker than the cephalic
vein.Our results demonstrate that both the diameter of the cephalic vein and the
anastomosis angle play a crucial role in order to obtain a regular blood dynamics that
could prevent fistula failure.In particular, when a high anastomosis angle is combined
with a large diameter of the cephalic vein, the recirculation regions and the low WSS
(wall shear stress) zones are reduced. Conversely, from a structural point of view, a
low anastomosis angle with a large diameter of the cephalic vein reduce the
mechanical stress acting on the vessel walls. |
-
17/2023 - 24/02/2023
Savin, M.S.; Cavinato, L.; Costa, G.; Fiz, F.; Torzilli, G.; Vigano', L.; Ieva, F.
Distant supervision for imaging-based cancer sub-typing in Intrahepatic Cholangiocarcinoma | Abstract | | Finding effective ways to perform cancer sub-typing is currently a trending research topic for therapy optimization and personalized medicine. Stemming from genomic field, several algorithms have been proposed. In the context of texture analysis, limited efforts have been attempted, yet imaging information is known to entail useful knowledge for clinical practice. We propose a distant supervision model for imaging-based cancer sub-typing in Intrahepatic Cholangiocarcinoma patients. A clinically informed stratification of patients is built and homogeneous groups of patients are characterized in terms of survival probabilities, qualitative cancer variables and radiomic feature description. Moreover, the contributions of the information derived from the ICC area and from the peritumoral area are evaluated. The findings suggest the reliability of the proposed model in the context of cancer research and testify the importance of accounting for data coming from both the tumour and the tumour-tissue interface. |
-
15/2023 - 22/02/2023
Ragni, A.; Masci, C.; Ieva, F.; Paganoni, A. M.
Clustering Hierarchies via a Semi-Parametric Generalized Linear Mixed Model: a statistical significance-based approach | Abstract | | We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within the family of semi-parametric mixed-effects models, a latent clustering structure of the highest-level units can be identified by assuming the random effects to follow a discrete distribution with an unknown number of support points. We achieve this by computing alpha-level confidence regions of the estimated support point and identifying statistically different clusters. At each iteration of a tailored Expectation Maximization algorithm, the two closest estimated support points for which the confidence regions overlap collapse. Unlike the related state-of-the-art methods that rely on arbitrary thresholds to determine the merging of close discrete masses, the proposed approach relies on conventional statistical confidence levels, thereby avoiding the use of discretionary tuning parameters. To demonstrate the effectiveness of our approach, we apply it to data from the Programme for International Student Assessment (PISA - OECD) to cluster countries based on the rate of innumeracy levels in schools. Additionally, a simulation study and comparison with classical parametric and state-of-the-art models are provided and discussed. |
-
13/2023 - 22/02/2023
Masci, C.; Cannistrà, M.; Mussida, P.
Modelling time-to-dropout via Shared Frailty Cox Models. A trade-off between accurate and early predictions | Abstract | | This paper investigates the student dropout phenomenon in a technical Italian university in a time-to-event perspective. Shared frailty Cox time-dependent models are applied to analyse the careers of students enrolled in different engineering programs with the aim of identifying the determinants of student dropout through time, to predict the time to dropout as soon as possible and to observe how the dropout phenomenon varies across time and degree programs. The innovative contributions of this work are methodological and managerial. First, the adoption of shared frailty Cox models with time-varying covariates is relatively new to the student dropout literature and it allows to take account of the student career evolution and of the heterogeneity across degree programs. Second, understanding the dropout pattern over time and identifying the earliest moment for obtaining its accurate prediction allow policy makers to set timely interventions for students at risk of dropout. |
-
11/2023 - 17/02/2023
Gatti, F.; de Falco, C.; Perotto, S.; Formaggia, L.
A parallel well-balanced numerical scheme for the simulation of fast landslides with efficient time stepping | Abstract | | We consider a single phase depth–averaged model for the numerical simulation of
fast–moving landslides with the goal of constructing a well-balanced positivitypreserving,
yet scalable and efficient, second–order time–stepping algorithm. We
apply a Strang splitting approach to distinguish between parabolic and hyperbolic
problems. For the parabolic case, we adopt a second–order Implicit–Explicit Runge–
Kutta–Chebyshev scheme, while we use a two–stage Taylor discretization combined
with a path-conservative strategy, to deal with the purely hyperbolic contribution.
The proposed strategy allows to combine these schemes in such a way that
the corresponding absolute stability regions remain unbiased, while guaranteeing
positivity-preserving and well-balancing property to the overall implementation.
The spatial discretization we adopt is based on a standard finite element method,
associated with a hierarchically refined Cartesian grid. After providing numerical
evidence of the well-balancing property, we demonstrate the capability of the proposed
approach in selecting time steps larger with respect to the ones adopted by
a classical Taylor-Galerkin scheme. Finally, we provide some meaningful scaling
results, both on ideal and realistic scenarios. |
-
10/2023 - 14/02/2023
Corti, M.; Antonietti, P.F.; Bonizzoni, F.; Dede', L., Quarteroni, A.
Discontinuous Galerkin Methods for Fisher-Kolmogorov Equation with Application to Alpha-Synuclein Spreading in Parkinson’s Disease | Abstract | | The spreading of prion proteins is at the basis of brain neurodegeneration. The paper deals with the numerical modelling of the misfolding process of alpha-synuclein in Parkinson’s disease. We introduce and analyze a discontinuous Galerkin method for the semi-discrete approximation of the Fisher-Kolmogorov (FK) equation that can be employed to model the process. We employ a discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) for space discretization, which allows us to accurately simulate the wavefronts typically observed in the prionic spreading. We prove stability and a priori error estimates for the semi-discrete formulation. Next, we use a Crank-Nicolson scheme to advance in time. For the numerical verification of our numerical model, we first consider a manufactured solution, and then we consider a case with wavefront propagation in two-dimensional polygonal grids. Next, we carry out a simulation of alpha-synuclein spreading in a two-dimensional brain slice in the sagittal plane with a polygonal agglomerated grid that takes full advantage of the flexibility of PolyDG approximation. Finally, we present a simulation in a three-dimensional patient-specific brain geometry reconstructed from magnetic resonance images. |
-
09/2023 - 10/02/2023
Buchwald, S.; Ciaramella, G.; Salomon, J.
Gauss-Newton oriented greedy algorithms for the reconstruction of operators in nonlinear dynamics | Abstract | | This paper is devoted to the development and convergence analysis of greedy reconstruction algorithms based on the strategy presented in [Y. Maday and J. Salomon, Joint Proceedings of the 48th IEEE Conference on
Decision and Control and the 28th Chinese Control Conference, 2009, pp. 375--379]. These procedures allow the design of a sequence of control functions that ease the
identification of unknown operators in nonlinear dynamical systems.
The original strategy of greedy reconstruction algorithms is based on an offline/online
decomposition of the reconstruction process and on an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent matrices. In the previous work [S. Buchwald, G. Ciaramella and J. Salomon, SIAM J. Control Optim., 59(6), pp. 4511-4537], convergence results were obtained in the case of linear identification problems. We tackle here the more general case of nonlinear systems. More precisely, we show that the controls obtained with the greedy algorithm on the corresponding linearized system lead to the local convergence of the classical Gauss-Newton method applied to the online nonlinear identification problem. We then extend this result to the controls obtained on nonlinear systems where a local convergence result is also obtained. The main convergence results are obtained for the reconstruction of drift operators in linear and bilinear dynamical systems. |
|
