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 1349 prodotti
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56/2026 - 25/06/2026
Botta, P.; Vitullo, P.; Ventimiglia, T.; Linninger, A.; Zunino, P.
Physics-Informed Learning of Microvascular Flow Models using Graph Neural Networks | Abstract | | The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a novel deep learning-based reduced-order modeling strategy, leveraging Graph Neural Networks (GNNs) trained on synthetic microvascular graphs to approximate hemodynamic quantities on anatomically realistic domains. Our method combines algorithms for synthetic vascular generation with a physics-informed training procedure that integrates graph topological information and local flow dynamics. To ensure the physical reliability of the learned surrogates, we incorporate a physics-informed loss functional derived from the governing equations, allowing enforcement of mass conservation and rheological constraints. The resulting GNN architecture demonstrates robust generalization capabilities across diverse network configurations. The GNN formulation is validated on benchmark problems with linear and nonlinear rheology, showing accurate pressure and velocity field reconstruction with substantial computational gains over full-order solvers. The methodology showcases significant generalization capabilities with respect to vascular complexity, as highlighted by tests on data from the mouse cerebral cortex. This work establishes a new class of graph-based surrogate models for microvascular flow, grounded in physical laws and equipped with inductive biases that mirror mass conservation and rheological models, opening new directions for real-time inference in vascular modeling and biomedical applications. |
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55/2026 - 23/06/2026
Beirao da Veiga, L.; Canuto, C.; Nochetto, R.H.; Vacc, G ; Verani, M.
A Virtual Element Method for elliptic problems on trimmed background meshes | Abstract | | We consider a two-dimensional piecewise $C^2$ domain that cuts through a quasi-uniform fixed polygonal background mesh, for instance made of quadrilaterals. A simple procedure based on convex hulls gives rise to a rather small number of polygonal boundary elements of various shapes, including elements with small edges and large aspect ratios; this is the computational mesh for a virtual element method (VEM), a trimmed background mesh. We classify all possible geometric configurations and study their stability and approximability properties. This entails deriving robust stabilization mechanisms and interpolation estimates for anisotropic elements and elements with small cuts, as well as a weak maximum principle for enhanced virtual elements; these contributions have intrinsic interest for VEM theory on geometric flexibility. We prove that the resulting VEM is uniformly stable in $H^1$, and also show optimal order-regularity error estimates in $H^1$ and $L^2$. Insightful numerical experiments corroborate and complement our theory. The proposed method is suitable for treating ALE formulations of problems in moving domains. |
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54/2026 - 23/06/2026
Antonietti, P. F.; Corti, M.; Leimer Saglio, C. B.; Pagani, S.
The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods | Abstract | | This work presents a new release of the lymph 2.0 library cite{antonietti_lymph_2025}, an open-source MATLAB framework for high-order discontinuous Galerkin discretizations on general polytopal meshes. The lymph 2.0 version is extended to support discretizations with element-wise polynomial approximation degrees, which allows the design of p-adaptive strategies based on a posteriori error indicators. In addition, the library introduces a unified assembly framework that abstracts the construction of discrete operators from the underlying physical model, improving code modularity, parallelism, maintainability, and extensibility. Moreover, the proposed approach enables shared-memory parallelism through dedicated parallel tools. Several numerical examples demonstrate the effectiveness of the proposed developments in reducing the computational cost while preserving approximation accuracy. |
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53/2026 - 23/06/2026
Dong Z., Jiang Y., Ng M., Ciaramella G., Yin J.
Chebyshev-Filtered Randomized Low-rank Preconditioners for Symmetric Positive Definite Linear Systems | Abstract | | Preconditioning is essential for accelerating Krylov methods for large symmet- ric positive definite (SPD) linear systems, especially when a small number of extremal eigenvalues deteriorate the convergence of preconditioned conjugate gradient (PCG) method. In this work, we propose a Chebyshev-filtered randomized low-rank preconditioning framework for SPD systems that targets spectral outliers at both ends of the spectrum of the coefficient matrices. The main idea is to use Chebyshev polynomial filtering to make the near-null eigenspace accessible to randomized subspace extraction. The filter amplifies the lower-tail eigencomponents that often govern PCG convergence, while randomized sketching recovers the amplified subspace using only a small number of matrix-matrix products. The resulting low-rank correction therefore targets small-eigenvalue components that are usually missed by standard randomized subspace extraction methods. The resulting preconditioner is algebraic and admits an efficient low-rank representation. We provide subspace error bounds for the filtered randomized extraction and derive condition-number estimates for the proposed preconditioning tech- niques. Numerical experiments demonstrate that the proposed method improves PCG convergence, especially when small eigenvalues are the main obstruction.
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52/2026 - 23/06/2026
Bonazzoli M.; Ciaramella G.; Mazzieri I.
On the Unmapped Tent Pitching for the Heterogeneous Wave Equation | Abstract | | The Unmapped Tent Pitching (UTP) algorithm is a space–time domain decomposition method for the parallel solution of hyperbolic problems. It was originally introduced for the homogeneous one-dimensional wave equation in [Ciaramella, Gander, Mazzieri, 2024]. UTP is inspired by the Mapped Tent Pitching (MTP) algorithm [Gopalakrishnan, Schöberl, Wintersteiger, 2017], which constructs the solution by iteratively building polytopal space–time subdomains, referred to as tents. In MTP, each physical tent is mapped onto a space–time rectangle, where local problems are solved before being mapped back to the original domain.
In contrast, UTP avoids the nonlinear and potentially singular mapping step by computing the solution directly on a physical space–time rectangle that contains the tent, at the expense of redundant computations in the region outside the tent. In this work, we investigate several strategies to extend UTP to heterogeneous media, where the wave propagation speed is piecewise constant over two subregions of the domain. Among the considered approaches, the most efficient in terms of computational time is the one employing space–time subdomains with identical spatial and temporal dimensions in both regions, determined by the maximum propagation speed. |
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51/2026 - 23/06/2026
Bellezza P.; Ciaramella G.; Macchini C.; Mazzieri I.; Verani M.
ParaFlow: Parareal Acceleration of Gradient-Flow Minimization | Abstract | | This work presents the ParaFlow class of optimization algorithms and its specific realization, the ParaFlowS algorithm. The ParaFlow framework employs the Parareal algorithm to enhance the convergence rate of gradient flows towards a minimum. The ParaFlowS method integrates the Parareal approach with (potentially stochastic) gradient descent (GD) method, resulting in a purely sequential optimization strategy. The proposed acceleration framework is assessed through extensive numerical experiments on unconstrained optimization problems associated with the training of fully connected neural networks. |
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50/2026 - 19/06/2026
Donnarumma, A.; Guagliardi, O.; Di Stazio F.; Mazza E.; Tanelli M.; Paganoni A.M.
Modelling Well-Being and Psychological Risk in Doctoral Education: An Integrated Latent Trait Approach | Abstract | | Doctoral education is increasingly recognized as a context in which psychological distress may emerge, shaped by
academic demands, institutional environments and interpersonal dynamics. However, evidence on how these latent
dimensions jointly configure doctoral well-being remains limited. This study investigates psychophysical well-being,
psychological risk indicators and perceived discrimination among PhD candidates at a large public Italian university,
using data from an anonymous voluntary questionnaire administered to doctoral researchers on well-being, academic
stress, institutional conditions, social support and doctoral experience.
Latent constructs of psychological well-being were extracted using Item Response Theory models: among the tested
specifications, the Four-Parameter Nested Logistic Regression Model (4PLnRM) provided the best empirical fit,
capturing heterogeneity in item response patterns and improving representation of the latent trait structure. Results
show that doctoral well-being is primarily driven by personal resources and perceived institutional quality, whereas
social support has a comparatively limited association, challenging conventional assumptions regarding the protective
role of peer networks in doctoral contexts.
With respect to perceived discrimination, a clear asymmetry emerges between vertical and horizontal dynamics.
Supervisor-related (“hierarchical”) discrimination is strongly associated with higher stress and poorer psychological
outcomes, particularly among women and candidates considering program withdrawal, while peer-related
(“horizontal”) discrimination shows weak associations. Overall, findings indicate that doctoral mental health is more
strongly associated with supervisory and institutional conditions than with informal support networks, suggesting that
improving doctoral well-being may require structural interventions targeting supervisory relationships and
institutional governance rather than relying exclusively on individual coping resources. |
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49/2026 - 17/06/2026
Bortolotti, T.; Troilo, R.; Casu, F.; Vantini, S.; Menafoglio, A.
Regularized covariance estimation from partially observed interferometric data | Abstract | | The Small BAseline Subset technique provides remote measurements of ground displacement with high spatial resolution, making it a key tool for monitoring geophysical processes in hazard-prone areas. An effective analysis of this type of data requires reliable estimation of their second-order structure, which is difficult to achieve because the measurements are systematically missing over relatively large portions of the investigated areas. We tackle the problem from a functional data analysis perspective and treat the observations as partially observed functional data with two-dimensional domain. To properly characterize the data, we introduce the fragmented regime of partial observation, where parts of the curves are systematically missing across replicates. For this regime, we propose a novel method for covariance estimation, formulating the task as a matrix completion problem with Laplacian regularization. The estimator is nonparametric and free of stationarity or isotropy assumptions. Extensive simulations show that our method achieves consistently low estimation error across a range of covariance structures. Application to ground displacement data relative to the Phlegraean Fields demonstrates its ability to recover meaningful spatial dependence patterns, highlighting its potential for environmental risk assessment and monitoring. |
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