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 1322 prodotti
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08/2026 - 20/01/2026
Micheletti, S.
Newmark time marching as a preconditioned iteration for large SPD linear systems | Abstract | | We revisit the classical idea of computing the solution of a large symmetric positive definite linear system as the steady state of an artificial transient dynamics. Starting from a second-order model with ``mass'' and ``damping'' operators, we show that the explicit Newmark scheme (beta=0) induces a family of stationary iterations for Au=b, with a natural residual form and a transparent role for the pair (M, C). This viewpoint unifies, within a single algebraic framework, time-marching solvers, preconditioned fixed-point iterations, and momentum-like recurrences. In particular, by choosing M as a preconditioner and using Rayleigh damping C = a_0 M + a_1 A, the induced iteration can be implemented efficiently via inexact inner solves and behaves as a robust preconditioned method for challenging diffusion problems. Numerical experiments on model elliptic operators illustrate the influence of (M, C) and provide practical parameter guidelines. |
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07/2026 - 14/01/2026
Corti, M.; Ahern, A.; Goriely, A.; Kuhl, E.; Antonietti, P.F.
A whole-brain model of amyloid beta accumulation and cerebral hypoperfusion in Alzheimer's disease | Abstract | | Accumulation of amyloid beta proteins is a defining feature of Alzheimer's disease, and is usually accompanied by cerebrovascular pathology. Evidence suggests that amyloid beta and cerebrovascular pathology are mutually reinforcing; in particular, amyloid beta suppresses perfusion by constricting capillaries, and hypoperfusion promotes the production of amyloid beta. Here, we propose a whole-brain model coupling amyloid beta and blood vessel through a hybrid model consisting of a reaction-diffusion system for the protein dynamics and porous--medium model of blood flow within and between vascular networks: arterial, capillary and venous. We discretize the resulting parabolic-elliptic system of PDEs by means of a high-order discontinuous Galerkin method in space and an implicit Euler scheme in time. Simulations in realistic brain geometries demonstrate the emergence of multistability, implying that a sufficiently large pathogenic protein seeds is necessary to trigger disease outbreak. Motivated by the "two-hit vascular hypothesis" of Alzheimer's disease that hypoperfusive vascular damage triggers amyloid beta pathology, we also demonstrate that localized hypoperfusion, in response to injury, can destabilize the healthy steady state and trigger brain-wide disease outbreak. |
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05/2026 - 13/01/2026
Ranno, A.; Ballarin, F.; Lespagnol, F.; Zunino, P.; Perotto, S.
A fictitious domain formulation based on hierarchical model reduction applied to drug-eluting stents | Abstract | | This paper presents a novel combination of the Fictitious Domain (FD) approach with the Hierarchical Model (HiMod) reduction for the simulation of the hemodynamics in an artery with a drug-eluting stent. Classical finite element methods are computationally expensive due to the geometrical complexity of stented arteries. The FD approach merges stent and lumen domains into a single computational domain, weakly imposing boundary conditions on the stent-lumen interface via Lagrange multipliers. However, the FD technique can lead to inaccurate solutions when dealing with non-conforming grids. In contrast, a HiMod formulation offers flexibility in tuning accuracy and computational cost but struggles with non-smooth domains like stented arteries. To address these limitations, we combine the FD and HiMod approaches, using a reduced stent-lumen interface condition to simplify implementation while maintaining accuracy. This combined approach is tested on an advection-diffusion equation to model drug elution into the bloodstream. For proof-of-concept, we use a simplified axisymmetric geometry comprising an idealized artery segment and a ring-shaped stent. Finally, we extend our analysis to include more realistic blood flow conditions and conduct a sensitivity analysis of drug concentration with respect to ring spacing. The numerical results demonstrate the effectiveness of the proposed approach. |
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06/2026 - 13/01/2026
Corti, M.; Gómez, S.
On the compact discontinuous Galerkin method for polytopal meshes | Abstract | | The Compact Discontinuous Galerkin method was introduced by Peraire and Persson in (SIAM J. Sci. Comput., 30, 1806--1824, 2008). In this work, we present the stability and convergence analysis for the~$hp$-version of this method applied to elliptic problems on polytopal meshes. Moreover, we introduce fast and practical algorithms that allow the CDG, LDG, and BR2 methods to be implemented within a unified framework. Our numerical experiments show that the CDG method yields a compact stencil for the stiffness matrix, with faster assembly and solving times compared to the LDG and BR2 methods. We numerically study how coercivity depends on the method parameters for various mesh types, with particular focus on the number of facets per mesh element. Finally, we demonstrate the importance of choosing the correct directions for the numerical fluxes when using variable polynomial degrees. |
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04/2026 - 12/01/2026
Ragni, A.; Cavinato, L.; Ieva, F.
Penalized Likelihood Optimization for Adaptive Neighborhood Clustering in Time-to-Event Data with Group-Level Heterogeneity | Abstract | | The identification of patient subgroups with comparable event-risk dynamics plays a key role in supporting informed decision-making in clinical research.
In such settings, it is important to account for the inherent
dependence that arises when individuals are nested within higher-level units, such as hospitals.
Existing survival models account for group-level heterogeneity through frailty terms but do not uncover latent patient subgroups, while most clustering methods ignore hierarchical structure and are not estimated jointly with survival outcomes. In this work, we introduce a new framework that simultaneously performs patient clustering and shared-frailty survival modeling through a penalized likelihood approach. The proposed methodology adaptively learns a patient-to-patient similarity matrix via a modified version of spectral clustering, enabling cluster formation directly from estimated risk profiles while accounting for group membership.
A simulation study highlights the proposed model's ability to recover latent clusters and to correctly estimate hazard parameters.
We apply our method to a large cohort of heart-failure patients hospitalized with COVID-19 between 2020 and 2021 in the Lombardy region (Italy), identifying clinically meaningful subgroups characterized by distinct risk profiles and highlighting the role of respiratory comorbidities and hospital-level variability in shaping mortality outcomes.
This framework provides a flexible and interpretable tool for risk-based patient stratification in hierarchical data settings. |
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03/2026 - 09/01/2026
Mapelli, A.; Carini, L.; Ieva, F.; Sommariva, S.
A neighbour selection approach for identifying differential networks in conditional functional graphical models | Abstract | | Estimation of brain functional connectivity from EEG data is of great importance both for medical research and diagnosis. It involves quantifying the conditional dependencies among the activity of different brain areas from the time-varying electric field recorded by sensors placed outside the scalp. These dependencies may vary within and across individuals and be influenced by covariates such as age, mental status, or disease severity. Motivated by this problem, we propose a novel neighbour selection approach based on functional-on-functional regression for the characterization of conditional Gaussian functional graphical models. We provide a fully automated, data-driven procedure for inferring conditional dependence structures among observed functional variables. In particular, pairwise interactions are directly identified and allowed to vary as a function of covariates, enabling covariate-specific modulation of connectivity patterns. Our proposed method accommodates an arbitrary number of continuous and discrete covariates. Moreover, unlike existing
methods for direct estimation of differential graphical models, the proposed approach yields directly interpretable coefficients, allowing discrimination between covariate-induced increases and decreases in interaction strength. The methodology is evaluated through extensive simulation studies and an application to experimental EEG data. The results demonstrate clear advantages over existing approaches, including
higher estimation accuracy and substantially reduced computational cost, especially in high-dimensional settings. |
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02/2026 - 08/01/2026
Antonietti, P.F.; Beirao da Veiga, L.; Botti, M.; Harnist, A.; Vacca, G.; Verani, M.
Virtual Element methods for non-Newtonian shear-thickening fluid flow problems | Abstract | | In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r >2) including both degenerate (delta= 0) and non-degenerate (delta > 0) cases. The proposed Virtual Element method features two distinguishing advantages: the construction of an exactly divergence-free discrete
velocity field and compatibility with general polygonal meshes. The analysis presented in this work extends the results of [55], where only shear-thinning behavior (1 < r < 2) was considered. Indeed, the theoretical
analysis of the shear-thickening setting requires several novel analytical tools, including: an infsup stability analysis of the discrete velocity-pressure coupling in non-Hilbertian norms, a stabilization term specifically
designed to address the nonlinear structure as the exponent r >2; and the introduction of a suitable discrete norm tailored to the underlying nonlinear constitutive relation. Numerical results demonstrate the practical performance of the proposed formulation. |
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01/2026 - 02/01/2026
Iapaolo V.; Vergani, A.M.; Cavinato, L.; Ieva, F.
Multi-view learning and omics integration: a unified perspective with applications to healthcare | Abstract | | Recent technological advances have made it possible to collect diverse biomedical data sources for each individual, ranging from imaging to genetics and digital health records.
Integrating such heterogeneous information in a coherent and informative way is a key challenge for modern biomedical data analysis. In this work, we present a unified perspective that bridges the fields of multi-view learning and multiomics integration, which have traditionally developed in parallel but share the same underlying objective. We organize this vast methodological landscape with respect to learning objectives, providing a structured overviewof core paradigms, associated challenges, and emerging directions. Through a case study on UK Biobank data, we highlight the importance of interpretability in biomedical contexts by applying two representative methods, AJIVE and SGCCA, which bridge the multi-omics and multi-viewlearning streams. The results show that integrative approaches provide more informative and clinically meaningful insights than single-view analyses, underscoring their practical relevance for biomedical research. |
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