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 1237 prodotti
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21/2025 - 28/04/2025
Caldera, L., Masci, C., Cappozzo, A., Forlani, M., Antonelli, B., Leoni, O., Ieva, F.
Uncovering mortality patterns and hospital effects in COVID-19 heart failure patients: a novel Multilevel logistic cluster-weighted modeling approach | Abstract | | Evaluating hospital performance and its relationship to patients' characteristics is of utmost importance to ensure timely, effective, and optimal treatment. This is particularly relevant in areas and situations where the healthcare system must deal with an unexpected surge in hospitalizations, such as heart failure patients in the Lombardy region of Italy during the COVID-19 pandemic. Motivated by this issue, the paper introduces a novel Multilevel Logistic Cluster-Weighted Model (ML-CWMd) for predicting 45-day mortality following hospitalization due to COVID-19. The methodology flexibly accommodates dependence patterns among continuous and dichotomous variables; effectively accounting for group-specific effects in distinct subgroups showing different attributes. A tailored Classification Expectation-Maximization algorithm is developed for parameter estimation, and extensive simulation studies are conducted to evaluate its performance against competing models. The novel approach is applied to administrative data from Lombardy Region, with the aim of profiling heart failure patients hospitalized for COVID-19 and investigating the hospital-level impact on their overall mortality.
A scenario analysis demonstrates the model's efficacy in managing multiple sources of heterogeneity, thereby yielding promising results in aiding healthcare providers and policy makers in the identification of patient-specific treatment pathways. |
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20/2025 - 24/04/2025
Botti, M.; Prada, D.; Scotti, A.; Visinoni, M.
Fully-Mixed Virtual Element Method for the Biot Problem | Abstract | | Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and stress field, as well as satisfying local mass and momentum conservation.
In this work, we focus on a novel four-fields Virtual Element discretization of Biot's equations. The stress symmetry is strongly imposed in the definition of the discrete space, thus avoiding the use of an additional Lagrange multiplier.
A complete a priori analysis is performed, showing the robustness of the proposed numerical method with respect to limiting material properties. The first order convergence of the lowest-order fully-discrete numerical method, which is obtained by coupling the spatial approximation with the backward Euler time-advancing scheme, is confirmed by a complete 3D numerical validation. A well known poroelasticity benchmark is also considered to assess the robustness properties and computational performance. |
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19/2025 - 17/04/2025
Bortolotti, T.; Wang, Y. X. R.; Tong, X.; Menafoglio, A.; Vantini, S.; Sesia, M.
Noise-Adaptive Conformal Classification with Marginal Coverage | Abstract | | Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated prediction sets with precise coverage guarantees for any classification model. However, its reliance on the idealized assumption of perfect data exchangeability limits its effectiveness in the presence of real-world complications, such as low-quality labels -- a widespread issue in modern large-scale data sets. This work tackles this open problem by introducing an adaptive conformal inference method capable of efficiently handling deviations from exchangeability caused by random label noise, leading to informative prediction sets with tight marginal coverage guarantees even in those challenging scenarios. We validate our method through extensive numerical experiments demonstrating its effectiveness on synthetic and real data sets, including CIFAR-10H and BigEarthNet. |
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18/2025 - 09/04/2025
Antonietti, P.F.; Corti, M.; Gómez, S.; Perugia, I.
A structure-preserving LDG discretization of the Fisher-Kolmogorov equation for modeling neurodegenerative diseases | Abstract | | This work presents a structure-preserving, high-order, unconditionally stable numerical method for approximating the solution to the Fisher-Kolmogorov equation on polytopic meshes, with a particular focus on its application in simulating misfolded protein spreading in neurodegenerative diseases. The model problem is reformulated using an entropy variable to guarantee solution positivity, boundedness, and satisfaction of a discrete entropy-stability inequality at the numerical level. The scheme combines a local discontinuous Galerkin method on polytopal meshes for the space discretization with a v-step backward differentiation formula for the time integration. Implementation details are discussed, including a detailed derivation of the linear systems arising from Newton's iteration. The accuracy and robustness of the proposed method are demonstrated through extensive numerical tests. Finally, the method's practical performance is demonstrated through simulations of alpha-synuclein propagation in a two-dimensional brain geometry segmented from MRI data, providing a relevant computational framework for modeling synucleopathies (such as Parkinson's disease) and, more generally, neurodegenerative diseases. |
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16/2025 - 04/04/2025
Radisic, I.; Regazzoni, F.; Bucelli, M.; Pagani, S.; Dede', L.; Quarteroni, A.
Influence of cellular mechano-calcium feedback in numerical models of cardiac electromechanics | Abstract | | Multiphysics and multiscale mathematical models enable the non-invasive study of cardiac function. These models often rely on simplifying assumptions that neglect certain biophysical processes to balance fidelity and computational cost. In this work, we propose an eikonal-based framework that incorporates mechano-calcium feedback -- the effect of mechanical deformation on calcium-troponin buffering -- while introducing only negligible computational overhead. To assess the impact of mechano-calcium feedback at the organ level, we develop a bidirectionally coupled cellular electromechanical model and integrate it into two cardiac multiscale frameworks: a monodomain-driven model that accounts for geometric feedback on electrophysiology and the proposed eikonal-based approach, which instead neglects geometric feedback. By ensuring consistent cellular model calibration across all scenarios, we isolate the role of mechano-calcium feedback and systematically compare its effects against models without it. Our results indicate that, under baseline conditions, mechano-calcium feedback has minimal influence on overall cardiac function. However, its effects become more pronounced in altered force generation scenarios, such as inotropic modulation. Furthermore, we demonstrate that the eikonal-based framework, despite omitting other types of mechano-electric feedback, effectively captures the role of mechano-calcium feedback at significantly lower computational costs than the monodomain-driven model, reinforcing its utility in computational cardiology. |
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17/2025 - 04/04/2025
Botti, M.; Mascotto, L.
Sobolev--Poincaré inequalities for piecewise $W^{1,p}$ functions over general polytopic meshes | Abstract | | We establish Sobolev-Poincaré inequalities for piecewise $W^{1,p}$ functions over sequences of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes in any dimension; amongst others, they cover the case of standard Poincaré inequalities for piecewise $W^{1,p}$ functions and can be useful in the analysis of nonconforming finite element discretizations of nonlinear problems. Crucial tools in their derivation are novel Sobolev-trace inequalities and Babuska-Aziz inequalities with mixed boundary conditions. We provide estimates that are constant free, i.e., that are fully explicit with respect to the geometric properties of the domain and the underlying sequence of polytopic meshes. |
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15/2025 - 14/03/2025
Fois, M.; de Falco, C.; Formaggia L.
Efficient particle generation for depth-averaged and fully 3D MPM using TIFF image data | Abstract | | In this work, we present a comprehensive framework for the generation and efficient management of particles in both fully three-dimensional (3D) and depth-averaged Material Point Method (DAMPM) simulations. Our approach leverages TIFF image data to construct initial conditions for large-scale geophysical flows, with a primary focus on landslide modeling. We describe the algorithms developed for particle initialization, distribution, and tracking, ensuring consistency and computational efficiency across different MPM formulations. The proposed methods enable accurate representation of complex topographies while maintaining numerical stability and adaptability to diverse material behaviors. Although the primary application is landslide simulation, the methodologies outlined are broadly applicable to other fields involving granular flows, fluid-structure interactions, and large-deformation processes. Performance evaluations demonstrate the efficiency and robustness of our approach, highlighting its potential for advancing high-fidelity simulations in geomechanics and beyond. |
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13/2025 - 28/02/2025
Scimone, R.; Menafoglio, A.; Secchi, P.
Estimating Non-Stationarity in Spatial Processes: an approach based on Random Domain Decomposition | Abstract | | The present work addresses the problem of flexible and efficient parameter estimation for non-stationary Gaussian random fields. This problem is crucial to enable modeling and stochastic simulation of complex natural phenomena in the Earth Sciences. Building on the non-stationary Matérn model of Paciorek and Schervish (2006), we propose a novel computational method that leverages random and repeated domain partitions to construct locally stationary estimates. Unlike existing approaches that rely on fixed grids of knots, our method employs a bagging-type strategy to mitigate the influence of domain decompositions in a divide-and-conquer fashion. This results in more robust and adaptive estimations, overcoming key limitations of traditional methods. Through extensive simulations and a real case study, we demonstrate that while fixed grids noticeably impact the final estimated models, our approach produces grid-free estimations, thanks to the additional source of randomness introduced by the aleatory partitions of the domain. |
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