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 1249 prodotti
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27/2025 - 10/05/2025
Antonietti P.F.; Artoni, A.; Ciaramella, G.; Mazzieri, I.
A review of discontinuous Galerkin time-stepping methods for wave propagation problems | Abstract | | This chapter reviews and compares discontinuous Galerkin time-stepping methods for the numerical approximation of second-order ordinary differential equations, particularly those stemming from space finite element discretization of wave propagation problems. Two formulations, tailored for second- and first-order systems of ordinary differential equations, are discussed within a generalized framework, assessing their stability, accuracy, and computational efficiency. Theoretical results are supported by various illustrative examples that validate the findings, enhancing the understanding and applicability of these methods in practical scenarios. |
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24/2025 - 08/05/2025
Bartsch, J.; Borzi, A.; Ciaramella, G.; Reichle, J.
Adjoint-based optimal control of jump-diffusion processes | Abstract | | Stochastic differential equations (SDEs) using jump-diffusion processes describe many natural phenomena at the microscopic level. Since they are commonly used to model economic and financial evolutions, the calibration and optimal control of such processes are of interest to many communities and have been the subject of extensive research. In this work, we develop an optimization method working at the microscopic level. This allows us also to reduce computational time since we can parallelize the calculations and do not encounter the so-called curse of dimensionality that occurs when lifting the problem to its macroscopic counterpart using partial differential equations (PDEs). Using a discretize-then- optimize approach, we derive an adjoint process and an optimality system in the Lagrange framework. Then, we apply Monte Carlo methods to solve all the arising equations. We validate our optimization strategy by extensive numerical experiments. We also successfully test a optimization procedure that avoids storing the information of the forward equation.
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22/2025 - 30/04/2025
Leimer Saglio, C. B.; Pagani, S.; Antonietti P. F.
A p-adaptive polytopal discontinuous Galerkin method for high-order
approximation of brain electrophysiology | Abstract | | Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal resolution. This paper introduces a novel p-adaptive discontinuous Galerkin method on polytopal grids (PolyDG) coupled with Crank–Nicolson time integration to approximate such models efficiently. The p-adaptive method enhances local accuracy via dynamic, element-wise polynomial refinement/de-refinement guided by a-posteriori error estimators. A novel clustering algorithm automatizes the selection of elements for adaptive updates, further improving efficiency. A wide set of numerical tests, including epileptic seizure simulations in a sagittal section of a human brain stem, demonstrate the method’s ability to reduce computational load while maintaining the accuracy of the numerical solution in capturing the dynamics of multiple wavefronts. |
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23/2025 - 30/04/2025
Antonietti, P. F.; Caldana, M.; Mazzieri, I.; Re Fraschini, A.
MAGNET: an open-source library for mesh agglomeration by Graph Neural Networks | Abstract | | We introduce MAGNET, an open-source Python library designed for mesh agglomeration in both two- and three-dimensions, based on employing Graph Neural Networks (GNN). MAGNET serves as a comprehensive solution for training a variety of GNN models, integrating deep learning and other advanced algorithms such as METIS and k-means to facilitate mesh agglomeration and quality metric computation. The library's introduction is outlined through its code structure and primary features. The GNN framework adopts a graph bisection methodology that capitalizes on connectivity and geometric mesh information via SAGE convolutional layers, in line with the methodology proposed by Antonietti et al. (2024). Additionally, the proposed MAGNET library incorporates reinforcement learning to enhance the accuracy and robustness of the model for predicting coarse partitions within a multilevel framework. A detailed tutorial is provided to guide the user through the process of mesh agglomeration and the training of a GNN bisection model. We present several examples of mesh agglomeration conducted by MAGNET, demonstrating the library's applicability across various scenarios. Furthermore, the performance of the newly introduced models is contrasted with that of METIS and k-means, illustrating that the proposed GNN models are competitive regarding partition quality and computational efficiency. Finally, we exhibit the versatility of MAGNET's interface through its integration with lymph, an open-source library implementing discontinuous Galerkin methods on polytopal grids for the numerical discretization of multiphysics differential problems. |
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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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