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 1253 prodotti
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23/2022 - 27/04/2022
Masci, C.; Ieva, F.; Paganoni, A.M.
A multinomial mixed-effects model with discrete random effects for modelling dependence across response categories | Abstract | | We propose a Semi-Parametric Mixed-Effects Multinomial regression model to deal with estimation and inference issues in the case of categorical and hierarchical data. The proposed modelling assumes the probability of each response category to be identified by a set of fixed and random effects parameters, estimated by means of an Expectation-Maximization algorithm. Random effects are assumed to follow a discrete distribution with an a priori unknown number of support points. For a K-category response, this method identifies a latent structure at the highest level of grouping, where groups are clustered into (K-1)-dimensional subpopulations. This method is an extension of the multinomial semi-parametric EM algorithm proposed in the literature, in which we relax the independence assumption across random-effects relative to different response categories. Since the category-specific random effects arise from the same subjects, their independence assumption is seldom verified in real data. In this sense, the proposed method properly models the natural data structure, as emerges by the results of simulation and case studies, which highlight the importance of taking into account the data dependence structure in real data applications. |
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22/2022 - 17/04/2022
Regazzoni, F.; Pagani, S.; Quarteroni, A.
Universal Solution Manifold Networks (USM-Nets): non-intrusive mesh-free surrogate models for problems in variable domains | Abstract | | We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our method employs a mesh-less architecture, thus overcoming the limitations associated with image segmentation and mesh generation required by traditional discretization methods. Indeed, we encode geometrical variability through scalar landmarks, such as coordinates of points of interest. In biomedical applications, these landmarks can be inexpensively processed from clinical images. Our approach is non-intrusive and modular, as we select a data-driven loss function. The latter can also be modified by considering additional constraints, thus leveraging available physical knowledge. Our approach can also accommodate a universal coordinate system, which supports the USM-Net in learning the correspondence between points belonging to different geometries, boosting prediction accuracy on unobserved geometries. Finally, we present two numerical test cases in computational fluid dynamics involving variable Reynolds numbers as well as computational domains of variable shape. The results show that our method allows for inexpensive but accurate approximations of velocity and pressure, avoiding computationally expensive image segmentation, mesh generation, or re-training for every new instance of physical parameters and shape of the domain. |
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21/2022 - 13/04/2022
Cappozzo, A.; Ieva, F.; Fiorito, G.
A general framework for penalized mixed-effects multitask learning with applications on DNA methylation surrogate biomarkers creation | Abstract | | Recent evidence highlights the usefulness of DNA methylation (DNAm) biomarkers as surrogates for exposure to risk factors for non-communicable diseases in epidemiological studies and randomized trials. DNAm variability has been demonstrated to be tightly related to lifestyle behavior and exposure to environmental risk factors, ultimately providing an unbiased proxy of an individual state of health. At present, the creation of DNAm surrogates relies on univariate penalized regression models, with elastic-net regularizer being the gold standard when accomplishing the task. Nonetheless, more advanced modeling procedures are required in the presence of multivariate outcomes with a structured dependence pattern among the study samples. In this work we propose a general framework for mixed-effects multitask learning in presence of high-dimensional predictors to develop a multivariate DNAm biomarker from a multi-center study. A penalized estimation scheme based on an expectation-maximization (EM) algorithm is devised, in which any penalty criteria for fixed-effects models can be conveniently incorporated in the fitting process. We apply the proposed methodology to create novel DNAm surrogate biomarkers for multiple correlated risk factors for cardiovascular diseases and comorbidities. We show that the proposed approach, modeling multiple outcomes together, outperforms state-of-the-art alternatives, both in predictive power and bio-molecular interpretation of the results. |
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20/2022 - 13/04/2022
Clementi, L.; Gregorio, C; Savarè, L.; Ieva, F; Santambrogio, M.D.; Sangalli, L.M.
A Functional Data Analysis Approach to Left Ventricular Remodeling Assessment | Abstract | | Left ventricular remodeling is a mechanism common to various cardiovascular diseases affecting myocardial morphology. It can be often overlooked in clinical practice since the parameters routinely employed in the diagnostic process (e.g., the ejection fraction) mainly focus on evaluating volumetric aspects. Nevertheless, the integration of a quantitative assessment of structural modifications can be pivotal in the early individuation of this pathology. In this work, we propose an approach based on functional data analysis to evaluate myocardial
contractility. A functional representation of ventricular shape is introduced, and functional principal component analysis and depth measures are used to discriminate healthy subjects from those affected by left ventricular hypertrophy. Our approach enables the integration of higher informative content compared to the traditional clinical parameters, allowing for a synthetic representation of morphological changes in the myocardium, which could be further explored and considered for future clinical practice implementation. |
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19/2022 - 11/04/2022
Lupo Pasini, M.; Perotto, S.
Hierarchical model reduction driven by machine learning for parametric advection-diffusion-reaction problems in the presence of noisy data | Abstract | | We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm.
In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach. |
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18/2022 - 11/04/2022
Bennati, L; Vergara, C; Giambruno, V; Fumagalli, I; Corno, A.F; Quarteroni, A; Puppini, G; Luciani, G.B
An image-based computational fluid dynamics study of mitral regurgitation in presence of prolapse | Abstract | | Purpose: In this work we performed an imaged-based computational
study of the systolic fluid dynamics in presence of Mitral Valve Regurgitation
(MVR). In particular, we compare healthy and different regurgitant
scenarios with the aim of quantifying different hemodynamic quantities.
Methods: We performed computational fluid dynamic (CFD) simulations
in the left ventricle, left atrium and aortic root, with a resistive
immersed method, a turbulence model, and with imposed systolic wall
motion reconstructed from Cine-MRI images, which allowed us to segment
also the mitral valve. For the regurgitant scenarios we considered
an increase of the heart rate and a dilation of the left ventricle.
Results: Our results highlighted that MVR gave rise to regurgitant
jets through the mitral orifice impinging against the atrial
walls and scratching against the mitral valve leading to high values
of Wall Shear Stresses (WSS) with respect to the healthy case.
Conclusion: CFD with prescribed wall motion and immersed mitral
valve revealed to be an effective tool to quantitatively describe hemodynamics
in the case of MVR and to compare different regurgitant
scenarios. Our findings highlighted in particular the presence of
transition to turbulence in the atrium and allowed us to quantify
some important cardiac indices such as cardiac output and WSS. |
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17/2022 - 11/04/2022
Regazzoni, F.
Stabilization of staggered time discretization schemes for 0D-3D fluid-structure interaction problems | Abstract | | In this paper we analyze the numerical oscillations affecting time-staggered schemes for 0D-3D fluid-structure interaction (FSI) problems, which arise e.g. in the field of cardiovascular modeling, and we propose a novel stabilized scheme that cures this issue. We study two staggered schemes. In the first one, the 0D fluid model prescribes the pressure to the 3D structural mechanics model and receives the flow. In the second one, on the contrary, the fluid model receives the pressure and prescribes the flow. These schemes are respectively known, in the FSI literature, as Dirichlet-Neumann and Neumann-Dirichlet schemes, borrowing these terms from domain decomposition methods, although here a single iteration is performed before moving on to the next time step. Should the fluid be enclosed in a cavity, the Dirichlet-Neumann scheme is affected by non-physical oscillations whose origin lies in the balloon dilemma, for which we provide an algebraic interpretation. Moreover, we show that also the Neumann-Dirichlet scheme can be unstable for a range of parameter choices. Surprisingly, increasing either the viscous dissipation or the inertia of the structure favours the onset of oscillations. Our analysis provides an explanation for this fact and yields sharp stability bounds on the time step size. Inspired by physical considerations on the onset of oscillations, we propose a numerically consistent stabilization term for the Neumann-Dirichlet scheme. We prove that our proposed stabilized scheme is absolutely stable for any choice of time step size. These results are verified by several numerical tests. Finally, we apply the proposed stabilized scheme to an important problem in cardiac electromechanics, namely the coupling between a 3D model and a closed-loop lumped-parameter model of blood circulation. In this setting, our proposed scheme successfully removes the non-physical oscillations that would otherwise affect the numerical solution. |
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16/2022 - 17/03/2022
G. Ciaramella, T. Vanzan
Substructured Two-grid and Multi-grid Domain Decomposition Methods | Abstract | | Two-level Schwarz domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corresponding smoothing iterative method), which is based on domain decomposition techniques, and a coarse correction step, which relies on a coarse space. The coarse space must properly represent the error components that the chosen one-level method is not capable to deal with. In
the literature, most of the works introduced efficient coarse spaces obtained as the span of functions defined on the entire space domain of the considered PDE. Therefore, the corresponding two-level preconditioners and iterative methods are defined in volume.
In this paper, we use the excellent smoothing properties of Schwarz domain decomposition methods to define, for general elliptic problems, a new class of substructured two-level methods, for which both Schwarz smoothers and coarse correction steps are defined on the interfaces (except for the application of the smoother that requires volumetric subdomain solves). This approach has several advantages. On the one hand, the required computational effort is cheaper than the one required by classical volumetric two-level methods. On the other hand,
our approach does not require, like classical multi-grid methods, the explicit construction of coarse spaces, and it permits a multilevel extension, which is desirable when the high dimension of the problem or the scarce quality of the coarse space prevents the efficient numerical solution. Numerical experiments demonstrate the effectiveness of the proposed new numerical framework. |
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