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 1346 prodotti
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63/2026 - 01/07/2026
Ciaramella, G.; Gong, W.; Kwok, F., Tan, Z.
Uniform Convergence of the Schwarz Alternating Method for Optimal Control Problems | Abstract | | In this paper, we analyze the Schwarz alternating method for unconstrained elliptic optimal control problems, which is equivalent to the corresponding method for the associated saddle-point systems. A distinctive feature in this setting is that the local error propagation operators are not necessarily nonexpansive in the energy norm, which stands in marked contrast to the standard elliptic boundary-value case. We develop a rigorous uniform convergence theory in the continuous setting and then extend the analysis to finite difference discretizations. In both formulations, we prove that the Schwarz iteration converges whenever its counterpart for the underlying elliptic equation is convergent. Furthermore, we show that the contraction factor for the auxiliary elliptic equation in the maximum norm provides a uniform upper bound, which is independent of the regularization parameter $alpha$, for the contraction factor of the optimal control iteration in the same norm. The theoretical framework is also extended to cover one-level alternating Schwarz and parallel Schwarz variants. Numerical experiments are presented to validate the theoretical results. |
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62/2026 - 01/07/2026
Ciaramella, G.; Gong, W.; Kwok, F.; Tan, Z.
On the Uniform Convergence Analysis of the Schwarz Alternating Method for Optimal Control Problems | Abstract | | In this paper, we investigate the uniform convergence of the Schwarz alternating method for unconstrained elliptic optimal control problems in one dimension. We derive the convergence factor of the method and find that the convergence factor of the method can be uniformly bounded by a factor ($<1$) associated with that for the state equation. We also observe that the local error propagation operators of the method under a standard choice of energy norms in the robust analysis of optimal control problems are nonexpansive. These observations indicate that the existing convergence analysis frameworks of domain decomposition methods for PDEs based on the standard choice of energy norms are not straightforwardly applicable to that for optimal control problems. |
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60/2026 - 01/07/2026
Ciaramella, G.; Gander, M.J.; Van Criekingen, S.; Vanzan, T.
Algebraic and Two-Level Parallel Substructured Schwarz Methods | Abstract | | Substructured Schwarz methods are interpretations of classical volume Schwarz methods as algorithms on interface variables. We introduce here a new parallel algebraic trace characterization to supersede the
geometric identification of the substructure within our petscs-based implementation of the parallel Schwarz method (equivalent to RAS).
We moreover consider a two-level substructured method with coarse space functions defined exclusively on the skeleton, and propose an additive version of the two-level preconditioner which significantly decreases the computing time. Weak scaling numerical results up to several thousands of CPU cores (one per subdomain) are presented
for the one- and two-level methods, comparing substructured and classical volume methods. |
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58/2026 - 30/06/2026
Mapelli, A.; Massi, M.C.; Cuccuru, G.; Di Angelantonio, E.; Ieva, F.
Prior-informed conditional Gaussian graphical models: an application to protein interaction network reconstruction | Abstract | | Motivation: Protein-protein interaction (PPI) networks, estimated from high-throughput omics data, foster biomarker discovery and precision medicine. Gaussian graphical models (GGMs) offer a principled reconstruction framework. Yet, existing applications face two limitations: they overlook the rich existing knowledge encoded in curated biological databases, and they assume a homogeneous network structure across all individuals, neglecting the influence of covariates or confounding factors on these interactions and preventing personalised representations. Even though these limitations have been addressed separately in previous work, no current approach resolves them simultaneously.
Results: We introduce a prior-informed conditional Gaussian graphical model that integrates database-derived interaction priors with covariate-dependent network modeling in a unified, scalable framework. The key methodological innovation is a structured, weighted penalty that selectively incorporates priors into population-level network estimation, while leaving context-specific perturbations entirely data-driven, as curated databases capture canonical interactions rather than disease-specific signals. Simulation studies demonstrate consistent and robust improvements in population-level network reconstruction across diverse settings, even when prior knowledge is imperfect. Applied to UK Biobank cardiometabolic proteomics (n = 49,129, p = 366 proteins), the method recovers T2D-associated network perturbations, identifying 34 network-central candidate biomarkers, several detectable only through their connectivity, not differential expression, and revealing six biologically coherent protein communities with distinct pathway enrichments spanning metabolic, cardiovascular, and cancer-related processes.
Availability and implementation: Code is available at https://github.com/AlessiaMapelli/Prior-informed-conditional-GGMs. |
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57/2026 - 29/06/2026
Fontana, N.; Secchi, P.; Di Angelantonio, E.; Ieva, F.
Modeling time-varying genetic effects on binary disease risk via functional Mendelian Randomization | Abstract | | Motivation: Genome-wide association studies have identified thousands of genetic variants associated with complex traits, establishing Mendelian Randomization (MR) as a powerful framework for causal inference using variants as natural experiments. However, existing MR methods treat causal effects as static, relying on cross-sectional exposure measurements and ignoring how genetic predispositions to disease operate dynamically across the life course. Recovering age-specific causal effect functions from longitudinal data requires combining functional data representations of exposure trajectories with instrumental variable estimation strategies suitable for binary disease endpoints, a methodological gap that has remained unaddressed.
Results: We develop a functional MR framework for binary outcomes that integrates Functional Principal Component Analysis with Two-Stage Residual Inclusion (2SRI), ensuring consistent estimation under the nonlinear logistic link function that renders standard instrumental variable estimators inconsistent. Simulations across different causal effect trajectory shapes, varying measurement densities, and varying instrument strengths demonstrate accurate recovery of time-varying genetically predicted effects with minimal bias. Applied to UK Biobank data, the framework identifies an age-specific causal effect of genetically predicted body mass index on type 2 diabetes risk concentrated in early mid-adulthood and progressively attenuating thereafter. Concordance between the proposed 2SRI estimator applied to type 2 diabetes and the established continuous-outcome functional MR estimator applied to the paired glycated haemoglobin marker in the same cohort provides indirect empirical support for the validity of the proposed approach.
Availability and implementation: The method is implemented in the R package mvfmr, with a full tutorial vignette. |
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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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