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 1308 prodotti
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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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82/2025 - 22/12/2025
Varetti, E.; Torzoni, M.; Tezzele, M.; Manzoni, A.
Adaptive digital twins for predictive decision-making: Online Bayesian learning of transition dynamics | Abstract | | This work shows how adaptivity can enhance value realization of digital twins in civil engineering. We focus on adapting the state transition models within digital twins represented through probabilistic graphical models. The bi-directional interaction between the physical and virtual domains is modeled using dynamic Bayesian networks. By treating state transition probabilities as random variables endowed with conjugate priors, we enable hierarchical online learning of transition dynamics from a state to another through effortless Bayesian updates. We provide the mathematical framework to account for a larger class of distributions with respect to the current literature. To compute dynamic policies with precision updates we solve parametric Markov decision processes through reinforcement learning. The proposed adaptive digital twin framework enjoys enhanced personalization, increased robustness, and improved cost-effectiveness. We assess our approach on a case study involving structural health monitoring and maintenance planning of a railway bridge. |
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81/2025 - 22/12/2025
Leimer Saglio, C. B.; Pagani, S.; Antonietti, P. F.
A massively parallel non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology | Abstract | | We investigate non-overlapping Schwarz preconditioners for the algebraic systems stemming from high-order discretizations of the coupled monodomain and Barreto-Cressman models, with applications to brain electrophysiology. The spatial discretization is based on a high-order Polytopal Discontinuous Galerkin (PolyDG) method, coupled with the Crank-Nicolson time discretization scheme with explicit extrapolation of the ion term. To improve solver efficiency, we consider additive Schwarz preconditioners within the PolyDG framework, which combines (massively parallel) local subdomain solvers with a coarse-grid correction. Numerical experiments demonstrate robustness with respect to the discretization parameters, as well as a significant reduction in iteration counts compared to the unpreconditioned solver. These features make the proposed approach well-suited for parallel large-scale simulations in brain electrophysiology. |
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79/2025 - 20/12/2025
Zacchei, F.; Conti, P.; Frangi, A.; Manzoni, A.
Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networks | Abstract | | Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial differential equations are involved, full-order models such as those based on the Finite Element Method can make traditional sampling approaches like Markov Chain Monte Carlo (MCMC) computationally infeasible. Although data-driven surrogate models may help reduce evaluation costs, their utility is often limited by the expense of generating high fidelity data. In contrast, low-fidelity data can be produced more efficiently, although relying on them alone may degrade the accuracy of the inverse UQ solution. To address these challenges, we propose a Multi-Fidelity Delayed Acceptance scheme for Bayesian inverse problems involving large-scale physics-based models. Extending the Multi-Level Delayed Acceptance framework, the method introduces multi-fidelity neural networks that combine the predictions of solvers of varying fidelity, with high-fidelity evaluations restricted to an offline training stage. During the online phase, likelihood evaluations are obtained by evaluating the coarse solvers and passing their outputs to the trained neural networks, thereby avoiding additional high-fidelity simulations. This construction allows heterogeneous coarse solvers to be incorporated consistently within the hierarchy, providing greater flexibility than standard Multi-Level Delayed Acceptance. The proposed approach improves the approximation accuracy of the low-fidelity solvers, leading to longer sub-chain lengths, better mixing, and accelerated posterior inference. The effectiveness of the strategy is demonstrated on two benchmark inverse problems involving (i) steady isotropic groundwater flow, (ii) an unsteady reaction-diffusion system, for which substantial computational savings are obtained. |
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78/2025 - 12/12/2025
Botti, M.; Mascotto, L.
Trace inequalities for piecewise W^1,p functions over general polytopic meshes | Abstract | | Trace inequalities are crucial tools to derive the stability of partial differential equations with inhomogeneous, natural boundary conditions. In the analysis of corresponding Galerkin methods, they are also essential to show convergence of sequences of discrete solutions to the exact one for data with minimal regularity under mesh refinements and/or degree of accuracy increase. In nonconforming discretizations, such as Crouzeix-Raviart and discontinuous Galerkin, the trial and test spaces consists of functions that are only piecewise continuous: standard trace inequalities cannot be used in this case. In this work, we prove several trace inequalities for piecewise W^{1,p} functions. Compared to analogous results already available in the literature, our inequalities are established:(i) on fairly general polytopic meshes (with arbitrary number of facets and arbitrarily small facets); (ii) without the need of finite dimensional arguments (e.g., inverse estimates, approximation properties of averaging operators); (iii) for different ranges of maximal and nonmaximal Lebesgue indices. |
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77/2025 - 11/12/2025
Bonetti, S.; Botti, M.; Vega, P.
A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity | Abstract | | In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the symmetry constraint on the stress field is imposed via penalization. This strategy is equivalent to adding a perturbation to the saddle point system arising when the stress symmetry is weakly imposed. The coupling of solid and fluid phases is discretized by means of stable mixed elements in space and implicit time advancing schemes. The presented stability analysis is fully robust with respect to meaningful cases of degenerate model parameters. Numerical tests validate the convergence and robustness and assess the performances of the method for the simulation of wave propagation phenomena in porous materials. |
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75/2025 - 05/12/2025
Crippa, B.; Scotti, A.; Villa, A.
A one-dimensional reduced plasma model for the electrical treeing | Abstract | | Plasma models, consisting of advection-diffusion Partial Differential Equations coupled with chemical reactions, are widely adopted to describe corona, streamers and dielectric barrier discharges. However, the complex geometry of the electrical treeing represents an obstacle for numerical simulations.
We develop a reduced one-dimensional formulation of a plasma model for the electrical treeing, describing the evolution of charge concentrations under the effect of an electric field. The reduced system consists of weakly coupled advection-diffusion-reaction equations for charge concentrations inside the treeing and on the dielectric surface, coupled with production-destruction Ordinary Differential Equations for the dipole moment.
A numerical scheme based on Finite Volumes and Patankar-type methods allows efficient simulations, while preserving key physical properties. The model is tested on increasingly complex geometries, from a straight line to a realistic electrical treeing. |
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