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 1238 prodotti
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35/2024 - 22/04/2024
Botti, L.; Botti, M.; Di Pietro, D.A.; Massa; F.C.
Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure | Abstract | | In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions that yield inf-sup stability as well as error estimates which distinguish the velocity- and pressure-related contributions to the error. We additionally identify the key properties under which the pressure-related contributions vanish in the estimate of the velocity,
thus leading to pressure-robustness. Several examples of existing and new schemes that fit into the framework are provided, and extensive numerical validation of the theoretical properties is provided. |
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34/2024 - 22/04/2024
Corti, M.
Exploring tau protein and amyloid-beta propagation: a sensitivity analysis of mathematical models based on biological data | Abstract | | Alzheimer's disease is the most common dementia worldwide. Its pathological development is well known to be connected with the accumulation of two toxic proteins: tau protein and amyloid-beta. Mathematical models and numerical simulations can predict the spreading patterns of misfolded proteins in this context. However, the calibration of the model parameters plays a crucial role in the final solution. In this work, we perform a sensitivity analysis of heterodimer and Fisher-Kolmogorov models to evaluate the impact of the equilibrium values of protein concentration on the solution patterns. We adopt advanced numerical methods such as the IMEX-DG method to accurately describe the propagating fronts in the propagation phenomena in a polygonal mesh of sagittal patient-specific brain geometry derived from magnetic resonance images. We calibrate the model parameters using biological measurements in the brain cortex for the tau protein and the amyloid-beta in Alzheimer's patients and controls. Finally, using the sensitivity analysis results, we discuss the applicability of both models in the correct simulation of the spreading of the two proteins. |
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32/2024 - 17/04/2024
Ziarelli, G.; Parolini, N.; Verani, M.
Learning epidemic trajectories through Kernel Operator Learning: from modelling to optimal control | Abstract | | Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consulted. In these complex epidemiological scenarios, machine learning architectures can play an important role, since they directly reconstruct data-driven models circumventing the specific modelling choices and the parameter calibration, typical of classical compartmental models. In this work, we discuss the efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics during epidemic outbreaks, where the transmission rate is ruled by an input strategy. In particular, we introduce two surrogate models, named KOL-m and KOL-$partial$, which reconstruct in two different ways the evolution of the epidemics. Moreover, we evaluate the generalization performances of the two approaches with different kernels, including the Neural Tangent Kernels, and compare them with a classical neural network model learning method. Employing synthetic but semi-realistic data, we show how the two introduced approaches are suitable for realizing fast and robust forecasts and scenario analyses, and how these approaches are competitive for determining optimal intervention strategies with respect to specific performance measures. |
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31/2024 - 27/03/2024
Gambarini, M.; Agate, G.; Ciaramella, G.; Miglio, E.; Maran, S.
Modeling and optimization for arrays of water turbine OWC devices | Abstract | | The large-scale implementation of wave energy conversion requires the installation of parks of devices.
We study the problem of optimizing park layout and control for wave energy converters of the oscillating water column type. As a test case, we consider a device with a Wells turbine working in water. First, a novel model based on a nonlinear ordinary differential equation is derived to describe the behavior of the water column and used to estimate the power matrix. Then, its linearization is derived in order to enable the fast simulation of large parks of devices.
The choice of the hydrodynamic model allows obtaining the gradient of the power with respect to the positions through an adjoint approach, making it especially convenient for optimization. We consider in particular the case of interaction with the piles of a floating wind energy plant.
The results from the developed computational framework allow us to draw interesting conclusions about park layout design. In particular, we observe that mutual interaction effects can be significant even in parks made up of devices of small size, and that wave reflection from the piles of an offshore structure can improve energy production. |
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30/2024 - 25/03/2024
Gregorio, C.; Rea, F.; Ieva, F.; Scagnetto, A.; Indennidade, C.; Cappelletto, C.; Di Lenarda, A.; Barbati, G.
Flexible approaches based on multi-state models and microsimulation to perform real-world cost-effectiveness analyses: an application to PCSK9-inhibitors | Abstract | | Objectives: This study aims to show the application of flexible statistical methods in real-world cost-effectiveness analyses applied in the cardiovascular field, focusing specifically on the use of PCSK9
inhibitors for hyperlipidaemia.
Methods: The proposed method allowed us to use an electronic health database to emulate a target trial for cost-effectiveness analysis using multi-state modelling and microsimulation. We formally
established the study design and provided precise definitions of the causal measures of interest, while also outlining the assumptions necessary for accurately estimating these measures using the available
data. Additionally, we thoroughly considered goodness-of-fit assessments and sensitivity analyses of the decision model, which are crucial to capture the complexity of individuals' healthcare pathway
and to enhance the validity of this type of health economic models.
Results: In the disease model, the Markov assumption was found to be inadequate, and a "time-reset" timescale was implemented together with the use of a time-dependent variable to incorporate past hospitalization history. Furthermore, the microsimulation decision model demonstrated a satisfying goodness-of-fit, as evidenced by the consistent results obtained in the short-term horizon
compared to a non-model-based approach. Notably, only in the long-term follow-up PCSK9 inhibitors revealed their favourable cost-effectiveness, with a minimum willingness-to-pay of 39,000
Euro/LY gained.
Conclusions: The approach demonstrated its significant utility in several ways. Unlike non-model based or alternative model-based methods, it enabled to 1) investigate long-term cost-effectiveness
comprehensively, 2) employ an appropriate disease model that aligns with the specific problem under study, and 3) conduct subgroup-specific cost-effectiveness analyses to gain more targeted insights.
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29/2024 - 19/03/2024
Palummo, A.;, Arnone, E.; Formaggia, L.; Sangalli, L.M.
Functional principal component analysis for incomplete space-time data | Abstract | | Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space-time data, when data may be affected by complex missing data structures. We formalise the problem in the framework of Functional Data Analysis, proposing an innovative method of functional Principal Component Analysis (fPCA) for incomplete space-time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a Majorize-Minimization approach, and we provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space-time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space-time fPCA to the study of the Lake Water Surface Temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an Essential Climate Variable. |
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28/2024 - 14/03/2024
Magri, M.; Riccobelli, D.
Modelling of initially stressed solids: structure of the energy density in the incompressible limit | Abstract | | This study addresses the modelling of elastic bodies, particularly when the relaxed configuration is unknown or non-existent. We adopt the theory of initially stressed materials, incorporating the deformation gradient and stress state of the reference configuration (initial stress tensor) into the response function. We show that for the theory to be applicable, the response function of the relaxed material is invertible up to an element of the material symmetry group. Additionally, we establish that commonly imposed constitutive restrictions, namely the initial stress compatibility condition and initial stress reference independence, naturally arise when assuming an initial stress generated solely from elastic distortion. The paper delves into modelling aspects concerning incompressible materials, showcasing the expressibility of strain energy density as a function of the deviatoric part of the initial stress tensor and the isochoric part of the deformation gradient. This not only reduces the number of independent invariants in the energy functional, but also enhances numerical robustness in finite element simulations. The findings of this research hold significant implications for modelling materials with initial stress, extending potential applications to areas such as mechanobiology, soft robotics, and 4D printing. |
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27/2024 - 07/03/2024
Antonietti, P.F.; Beirao da Veiga, L.; Botti, M.; Vacca, G.; Verani, M.
A Virtual Element method for non-Newtonian fluid flows | Abstract | | In this paper, we design and analyze a Virtual Element discretization for the steady motion of non-Newtonian, incompressible fluids. A specific stabilization, tailored to mimic the monotonicity and boundedness properties of the continuous operator, is introduced and theoretically investigated. The proposed method has several appealing features, including the exact enforcement of the divergence free condition and the possibility of making use of fully general polygonal meshes. A complete well-posedness and convergence analysis of the proposed method is presented under mild assumptions on the non-linear laws, encompassing common examples such as the Carreau–Yasuda model. Numerical experiments validating the theoretical bounds as well as demonstrating the practical capabilities of the proposed formulation are presented. |
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