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 1275 prodotti
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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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14/2025 - 28/02/2025
Nicolussi, F.; Masci, C.
Stratified Multilevel Graphical Models: Examining Gender Dynamics in Education | Abstract | | This study proposes a methodological approach to investigate gender disparities in education, particularly focusing on the schooling phase and its influence on career trajectories. The research applies multilevel linear models to analyse student performance concerning various factors, with a specific emphasis on gender-specific outcomes.
The study aims to identify and test context-specific independencies that may impact educational disparities between genders. The methodology includes the introduction of supplementary parameters in multilevel models to capture and examine these independencies. Furthermore, the research proposes encoding these novel relationships in graphical models, specifically stratified chain graph models, to visualize and generalize the complex dependencies among covariates, random effects, and gender influences on educational outcomes. |
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12/2025 - 26/02/2025
Alessandro Andrea Zecchi, Claudio Sanavio, Simona Perotto e Sauro Succi
Improved amplitude amplification strategies for the quantum simulation of classical transport problems | Abstract | | The quantum simulation of classical fluids often involves the use of probabilistic algorithms that encode the result of the dynamics in the form of the amplitude of the selected quantum state. In most cases, however, the amplitude probability is too low to allow an efficient use of these algorithms, thereby hindering the practical viability of the quantum simulation. The oblivious amplitude amplification algorithm is often presented as a solution to this problem, but to no avail for most classical problems, since its applicability is limited to unitary dynamics. In this paper, we show analytically that oblivious amplitude amplification when applied to non-unitary dynamics leads to a distortion of the quantum state and to an accompanying error in the quantum update. We provide an analytical upper bound of such error as a function of the degree of non-unitarity of the dynamics and we test it against a quantum simulation of an advection-diffusion-reaction equation, a transport problem of major relevance in science and engineering. Finally, we also propose an amplification strategy that helps mitigate the distortion error, while still securing an enhanced success probability. |
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