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 1319 prodotti
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13/2026 - 05/02/2026
Dimola, N.; Coclite, A.; Zunino, P.
Neural Preconditioning via Krylov Subspace Geometry | Abstract | | We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). Such systems are typically ill-conditioned due to embedded lower-dimensional structures and are solved using Krylov subspace methods. Our approach yields an approximation of the inverse operator employing a learning algorithm consisting of a two-stage training framework: an initial static pretraining phase, based on residual minimization, followed by a dynamic fine-tuning phase that incorporates solver convergence dynamics into the training process via a novel loss functional. This dynamic loss is defined by the principal angles between the residuals and the Krylov subspaces. It is evaluated using a differentiable implementation of the Flexible GMRES algorithm, which enables backpropagation through both the Arnoldi process and Givens rotations. The resulting neural preconditioner is explicitly optimized to enhance early-stage convergence and reduce iteration counts across a family of 3D–1D mixed-dimensional problems exhibiting geometric variability in the 1D domain. Numerical experiments show that our solver-aligned approach significantly improves convergence rate, robustness, and generalization.
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12/2026 - 02/02/2026
Corbetta A; Logan K.M.; Ferro M; Zuccolo L; Perola M.; Ganna A.; Di Angelantionio E.;Ieva F.
Longitudinal patterns of statin adherence and factors associated with decline in over one million individuals in Finland and Italy | Abstract | | Medication adherence is critical for effective management of chronic diseases and reducing healthcare burdens. Statins, commonly prescribed for cardiovascular disease prevention, require sustained, lifelong adherence, yet maintaining long-term adherence remains a significant challenge. Here, we analysed longitudinal population-wide electronic health records from over one million statin users in Finland and Italy to characterise adherence trajectories and their determinants. Using functional data analysis, we identified five distinct adherence patterns, with consistently high adherence being the most prevalent across both populations. Younger age, socioeconomic vulnerability, and statin use for primary prevention were consistently associated with a higher risk of declining adherence over time. Sex differences were observed in Italy but not in Finland, where divorced status and health-related educational background were also associated with declining adherence. Despite differences in healthcare systems, several factors were consistent across countries. These findings point to common behavioural drivers of long-term statin use and suggest that targeted, population-level interventions could better sustain adherence over time. |
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11/2026 - 31/01/2026
Cicalese, G.; Ciaramella, G.; Mazzieri, I.; Gander, M. J.
Optimized Schwarz Waveform Relaxation for the Damped Wave Equation | Abstract | | The performance of Schwarz Waveform Relaxation is critically dependent on the choice of transmission conditions. While classical absorbing conditions work well for wave propagation, they prove insufficient for damped wave equations, particularly in viscoelastic damping regimes where convergence becomes prohibitively slow. This paper addresses this limitation by introducing a more general transmission operator with two free parameters for the one-dimensional damped wave equation. Through frequency-domain analysis, we derive an explicit expression for the convergence factor governing the convergence rate. We propose and compare two optimization strategies, L-infinity and L-2 minimization, for determining optimal transmission parameters. Numerical experiments demonstrate that our optimized approach significantly accelerates convergence compared to standard absorbing conditions, especially for viscoelastic damping cases. The method provides a computationally efficient alternative to exhaustive parameter search while maintaining robust performance across different damping regimes. |
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10/2026 - 29/01/2026
Dimola, N.; Franco, N. R.; Zunino, P.
Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner | Abstract | | Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the computational workload increases considerably when attempting to accurately capture the behavior of the system under significant variations or uncertainties in the low-dimensional structures such as fractures, fibers, or vascular networks, due to the inevitable necessity of running multiple simulations. In this work, we present a novel preconditioning strategy that leverages neural networks and unsupervised operator learning to design an efficient preconditioner specifically tailored to a class of 3D-1D mixed-dimensional PDEs. The proposed approach is capable of generalizing to varying shapes of the 1D manifold without retraining, making it robust to changes in the 1D graph topology.
Moreover, thanks to convolutional neural networks, the neural preconditioner can adapt over a range of increasing mesh resolutions of the discrete problem, enabling us to train it on low resolution problems and deploy it on higher resolutions.
Numerical experiments validate the effectiveness of the preconditioner in accelerating convergence in iterative solvers, demonstrating its appeal and limitations over traditional methods. This study lays the groundwork for applying neural network-based preconditioning techniques to a broader range of coupled multi-physics systems. |
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09/2026 - 28/01/2026
Manzoni, V.; Ieva, F.;Larranaga, A.C.; Vetrano, D.L.; Gregorio, C.
Hidden multistate models to study multimorbidity trajectories | Abstract | | Multimorbidity in older adults is common, heterogeneous, and highly dynamic, and it is strongly associated with disability and increased healthcare utilization. However, existing approaches to studying multimorbidity trajectories are largely descriptive or rely on discrete-time models, which struggle to handle irregular observation intervals and right-censoring. We developed a continuous-time hidden multistate modeling framework to capture transitions among latent multimorbidity patterns while accounting for interval censoring and misclassification. A simulation study compared alternative model specifications under varying sample sizes and follow-up schemes, and the best-performing specification was applied to longitudinal data from the Swedish National Study on Aging and Care–Kungsholmen (SNAC-K), including 2,716 multimorbid participants followed for up to 18 years. Simulation results showed that hidden multistate models substantially reduced bias in transition hazard estimates compared to non-hidden models, with fully time-inhomogeneous models outperforming piecewise approximations. Application to SNAC-K confirmed the feasibility and practical utility of this framework, enabling identification of risk factors for accelerated progression toward complex multimorbidity and revealing a gradient of mortality risk across patterns. Continuous-time hidden multistate models provide a robust alternative to traditional approaches, supporting individualized predictions and informing targeted interventions and secondary prevention strategies for multimorbidity in aging populations. |
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08/2026 - 20/01/2026
Micheletti, S.
Newmark time marching as a preconditioned iteration for large SPD linear systems | Abstract | | We revisit the classical idea of computing the solution of a large symmetric positive definite linear system as the steady state of an artificial transient dynamics. Starting from a second-order model with ``mass'' and ``damping'' operators, we show that the explicit Newmark scheme (beta=0) induces a family of stationary iterations for Au=b, with a natural residual form and a transparent role for the pair (M, C). This viewpoint unifies, within a single algebraic framework, time-marching solvers, preconditioned fixed-point iterations, and momentum-like recurrences. In particular, by choosing M as a preconditioner and using Rayleigh damping C = a_0 M + a_1 A, the induced iteration can be implemented efficiently via inexact inner solves and behaves as a robust preconditioned method for challenging diffusion problems. Numerical experiments on model elliptic operators illustrate the influence of (M, C) and provide practical parameter guidelines. |
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07/2026 - 14/01/2026
Corti, M.; Ahern, A.; Goriely, A.; Kuhl, E.; Antonietti, P.F.
A whole-brain model of amyloid beta accumulation and cerebral hypoperfusion in Alzheimer's disease | Abstract | | Accumulation of amyloid beta proteins is a defining feature of Alzheimer's disease, and is usually accompanied by cerebrovascular pathology. Evidence suggests that amyloid beta and cerebrovascular pathology are mutually reinforcing; in particular, amyloid beta suppresses perfusion by constricting capillaries, and hypoperfusion promotes the production of amyloid beta. Here, we propose a whole-brain model coupling amyloid beta and blood vessel through a hybrid model consisting of a reaction-diffusion system for the protein dynamics and porous--medium model of blood flow within and between vascular networks: arterial, capillary and venous. We discretize the resulting parabolic-elliptic system of PDEs by means of a high-order discontinuous Galerkin method in space and an implicit Euler scheme in time. Simulations in realistic brain geometries demonstrate the emergence of multistability, implying that a sufficiently large pathogenic protein seeds is necessary to trigger disease outbreak. Motivated by the "two-hit vascular hypothesis" of Alzheimer's disease that hypoperfusive vascular damage triggers amyloid beta pathology, we also demonstrate that localized hypoperfusion, in response to injury, can destabilize the healthy steady state and trigger brain-wide disease outbreak. |
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05/2026 - 13/01/2026
Ranno, A.; Ballarin, F.; Lespagnol, F.; Zunino, P.; Perotto, S.
A fictitious domain formulation based on hierarchical model reduction applied to drug-eluting stents | Abstract | | This paper presents a novel combination of the Fictitious Domain (FD) approach with the Hierarchical Model (HiMod) reduction for the simulation of the hemodynamics in an artery with a drug-eluting stent. Classical finite element methods are computationally expensive due to the geometrical complexity of stented arteries. The FD approach merges stent and lumen domains into a single computational domain, weakly imposing boundary conditions on the stent-lumen interface via Lagrange multipliers. However, the FD technique can lead to inaccurate solutions when dealing with non-conforming grids. In contrast, a HiMod formulation offers flexibility in tuning accuracy and computational cost but struggles with non-smooth domains like stented arteries. To address these limitations, we combine the FD and HiMod approaches, using a reduced stent-lumen interface condition to simplify implementation while maintaining accuracy. This combined approach is tested on an advection-diffusion equation to model drug elution into the bloodstream. For proof-of-concept, we use a simplified axisymmetric geometry comprising an idealized artery segment and a ring-shaped stent. Finally, we extend our analysis to include more realistic blood flow conditions and conduct a sensitivity analysis of drug concentration with respect to ring spacing. The numerical results demonstrate the effectiveness of the proposed approach. |
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