MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1238 products
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06/2025 - 01/17/2025
Torzoni, M.; Manzoni, A.; Mariani, A.
Enhancing Bayesian model updating in structural health monitoring via learnable mappings | Abstract | | In the context of structural health monitoring (SHM), the selection and extraction of damage sensitive features from raw sensor recordings represent a critical step towards solving the inverse problem underlying the structural health identification. This work introduces a new way to enhance stochastic approaches to SHM through the use of deep neural networks. A learnable feature extractor and a feature-oriented surrogate model are synergistically exploited to evaluate a likelihood function within a Markov chain Monte Carlo sampling algorithm. The feature extractor undergoes a supervised pairwise training to map sensor recordings onto a low-dimensional metric space, which encapsulates the sensitivity to structural health parameters. The surrogate model maps the structural health parameters onto their feature description. The procedure enables the updating of beliefs about structural health parameters, effectively replacing the need for a computationally expensive numerical (finite element) model. A preliminary offline phase involves the generation of a labeled dataset to train both the feature extractor and the surrogate model. Within a simulation-based SHM framework, training vibration responses are cost-effectively generated by means of a multi-fidelity surrogate modeling strategy to approximate sensor recordings under varying damage and operational conditions. The multi-fidelity surrogate exploits model order reduction and artificial neural networks to speed up the data generation phase while ensuring the damage-sensitivity of the approximated signals. The proposed strategy is assessed through three synthetic case studies, demonstrating remarkable results in terms of accuracy of the estimated quantities and computational efficiency. |
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05/2025 - 01/15/2025
Buchwald, S.; Ciaramella, G.; Verani, M.
Greedy reconstruction algorithms for function approximation | Abstract | | Two key elements in any function approximation problem are the selection of data points and the choice of the structure of the ansatz within a given family of approximation functions. This paper is devoted to the development and analysis of greedy reconstruction algorithms that address both aspects to improve approximation accuracy and efficiency. The general idea of these methods is to select an optimal set of data points while simultaneously identifying a minimal structure that is able to accurately approximate the selected data. Theoretical and numerical studies on polynomial interpolation and function approximation by neural networks demonstrate the efficiency of the proposed algorithms. |
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04/2025 - 01/15/2025
Andrini, D.; Magri, M.; Ciarletta, P.
Nonlinear morphoelastic theory of biological shallow shells with initial stress | Abstract | | Shallow shells are widely encountered in biological structures, especially during embryogenesis, when they undergo significant shape variations. As a consequence of geometric frustration caused by underlying biological processes of growth and remodeling, such thin and moderately curved biological structures experience initial stress even in the absence of an imposed deformation. In this work, we perform a rigorous asymptotic expansion from three-dimensional elasticitiy to obtain a nonlinear morphoelastic theory for shallow shells accounting for both initial stress and large displacements. By application of the principle of stationary energy for admissible variation of the tangent and normal displacement fields with respect to the reference middle surface, we derive two generalised nonlinear equilibrium equations
of the Marguerre-von K´arm´an type. We illustrate how initial stress distributions drive the emergence of spontaneous mean and Gaussian curvatures which are generally not compatible with the existence of a stress free configuration. We also show how such spontaneous curvatures influence the structural behavior in the solutions of two systems: a saddle-like and a cylindrical shallow shell. |
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02/2025 - 01/08/2025
Corda, A.; Pagani, S.; Vergara, C.
Influence of patient-specific acute myocardial ischemia maps on arrhythmogenesis: a computational study | Abstract | | The early phase of acute myocardial ischemia is associated with an elevated risk of ventricular reentrant arrhythmias. After partial or total occlusion of a coronary artery, some regions of the heart experience a reduction in myocardial blood flow. This causes metabolic and cellular processes, such as hypoxia, hyperkalemia and acidosis, which lead to changes in the transmembrane ionic dynamics. The effect of such alterations may result in the formation of electrical loops and reentries.
In this context, digital twins aim at predicting patient-specific arrhythmic propensity to support clinical decision. Due to a lack of available representative data of acute events, digital twins can only rely on differential multiscale models, whose parameters are personalized based on imaging data. Through their numerical approximation, we can quantitatively assess arrhythmic risk by simulating the generation of arrhythmic episodes, possibly persistent, triggered by ectopic beats and in presence of acute myocardial regions. Since quantitative information (extent, localization, ...) about acute ischemic regions are hardly available from clinics, to date, computational models only integrate imaging data from chronic infarcted ventricles. This may not accurately reflect the acute condition. This work presents a novel patient-specific electrophysiological model, based on myocardial blood flow maps acquired during a pharmacologically induced acute ischemic event. The model personalization is obtained with the partitioning of the left ventricle geometries on the basis of the myocardial blood flow maps. First, we aim to numerically investigate the induction and sustainment of reentrant drivers in patient-specific scenarios, in order to assess their arrhythmic propensity. Secondly, we perform an intra-patient sensitivity analysis, where different levels of acute ischemia are virtually depicted for the most arrhythmogenic patient. Our results suggest that the amount of ischemic regions seems to have less influence on arrhythmogenesis than their pattern. |
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01/2025 - 01/04/2025
Dede', L.; Parolini, N.; Quarteroni, A.; Villani, G.; Ziarelli, G.
SEIHRDV: a multi-age multi-group epidemiological model and its validation on the COVID-19 epidemics in Italy | Abstract | | We propose a novel epidemiological model, referred to as SEIHRDV, for the numerical simulation of the COVID-19 epidemic, which we validate using data from Italy starting in September 2020. SEIHRDV features the following compartments: Susceptible (S), Exposed (E), Infectious (I), Healing (H), Recovered (R), Deceased (D) and Vaccinated (V). The model is age-stratified, as it considers the population split into 15 age groups. Moreover, it takes into account 7 different contexts of exposition to the infection (family, home, school, work, transport, leisure, other contexts), which impact on the transmission mechanism. Thanks to these features, the model can address the analysis of the epidemics and the efficacy of non-pharmaceutical interventions, as well as possible vaccination strategies and the introduction of the Green Pass, a containment measure introduced in Italy in 2021. By leveraging on the SEIHRDV model, we successfully analyzed epidemic trends during the COVID-19 outbreak from September 2020 to July 2021. The model proved instrumental in conducting comprehensive what-if studies and scenario analyses tailored to Italy and its regions. Furthermore, SEIHRDV facilitated accurate forecasting of the future potential trajectory of the epidemic, providing critical information for informed decision making and public health strategies. |
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108/2024 - 12/27/2024
Arostica, R.; Nolte, D.; Brown, A.; Gebauer, A.; Karabelas, E.; Jilberto, J.; Salvador, M.; Bucelli, M.; Piersanti, R.; Osouli, K.; Augustin, C.; Finsberg, H.; Shi, L.; Hirschvogel, M.; Pfaller, M.; Africa, P.C.; Gsell, M.; Marsden, A.; Nordsletten, D.; Regazzoni, F.; Plank, G.; Sundnes, J.; Dede’, L.; Peirlinck, M.; Vedula, V.; Wall, W.; Bertoglio, C.
A software benchmark for cardiac elastodynamics | Abstract | | In cardiovascular mechanics, reaching consensus in simulation results within a physiologically relevant range of parameters is essential for reproducibility purposes. Although currently available benchmarks contain some of the features that cardiac mechanics models typically include, some important modeling aspects are missing. Therefore, we propose a new set of cardiac benchmark problems and solutions for assessing passive and active material behaviour, viscous effects, and pericardial boundary condition. The problems proposed include simplified analytical fiber definitions and active stress models on a monoventricular and biventricular domains, allowing straightforward testing and validation with already developed solvers. |
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109/2024 - 12/27/2024
Liverotti, L.; Ferro, N.; Matteucci, M.; Perotto, S.
A PCA and mesh adaptation-based format for high compression of Earth Observation optical data with applications in agriculture | Abstract | | Earth Observation optical data are critical for agriculture, supporting tasks like vegetation health monitoring, crop classification, and land use analysis. However, the large size of multispectral and hyperspectral datasets poses challenges for storage, transmission, and processing, particularly in precision farming and resource-limited contexts. This work presents the H²-PCA-AT (Hilbert and Huffman-encoded Principal Component Analysis-Adaptive Triangular) format, a novel lossy compression framework that combines PCA for spectral reduction with anisotropic mesh adaptation for spatial compression. Adaptive triangular meshes capture image features with fewer elements with respect to a standard pixel grid, while efficient encoding with Hilbert curves and Huffman coding ensures compact storage. Numerical evaluations on data reconstruction, vegetation index computation, and land cover classification demonstrate the H²-PCA-AT format effectiveness, achieving superior compression compared to JPEG while preserving essential agricultural insights. |
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110/2024 - 12/27/2024
Pederzoli, V.; Corti, M.; Riccobelli, D.; Antonietti, P.F.
A coupled mathematical and numerical model for protein spreading and tissue atrophy, applied to Alzheimer's disease | Abstract | | The aim of this paper is to introduce, analyse and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by pathogen diffusion, with applications to neurodegenerative disorders. This study introduces a novel mathematical and computational model comprising a Fisher-Kolmogorov equation for species diffusion coupled with an elasticity equation governing mass loss. These equations intertwine through a logistic law dictating the reduction of the medium's mass. One potential application of this model lies in understanding the onset and development of Alzheimer's disease. Here, the equations can describe the propagation of misfolded tau-proteins and the ensuing brain atrophy characteristic of the disease. To address numerically the inherited complexities, we propose a Polygonal Discontinuous Galerkin method on polygonal/polyhedral grids for spatial discretization, while time integration relies on the theta-method. We present the mathematical model, delving into its characteristics and propose discretization applied. Furthermore, convergence results are presented to validate the model, accompanied by simulations illustrating the application scenario of the onset of Alzheimer's disease. |
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