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 1287 prodotti
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39/2019 - 16/10/2019
Lovato, I.; Pini, A.; Stamm, A.; Taquet, M.; Vantini, S.
Multiscale null hypothesis testing for network-valued data: analysis of brain networks of patients with autism | Abstract | | Networks are a natural way of representing the human brain for studying its structure and function and, as such, have been extensively used. In this view, case-control studies for understanding autism pertain to comparing samples of healthy and autistic brain networks. In order to understand the biological mechanisms involved in the pathology, it is key to localize the differences on the brain network. Motivated by this question, we hereby propose a general non-parametric finite-sample exact statistical framework that allows to test for differences in connectivity within and between pre-specified areas inside the brain network, with strong control of the family-wise error rate. We demonstrate unprecedented ability to differentiate children with non-syndromic autism from children with both autism and tuberous sclerosis complex using EEG data. The implementation of the method is available in the R package nevada. |
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37/2019 - 30/09/2019
Menafoglio, A.; Secchi, P.
O2S2: a new venue for computational geostatistics | Abstract | | Applied sciences have witnessed an explosion of georeferenced data. Object oriented spatial statistics (O2S2) is a recent system of ideas that provides a solid framework where the new challenges posed by the GeoData revolution can be faced, by grounding the analysis on a powerful geometrical and topological approach. We shall present a perspective on O2S2, as a fruitful ground where novel computational approaches to geosciences can be developed, at the very interface among varied fields of applied sciences – including mathematics, statistics, computer science and engineering.
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36/2019 - 30/09/2019
Salvador, M.; Dede', L.; Quarteroni, A.
An intergrid transfer operator using radial basis functions with application to cardiac electromechanics | Abstract | | In the framework of efficient partitioned numerical schemes for simulating multiphysics PDE problems, we propose using intergrid transfer operators based on radial basis functions to exchange accurately information between different PDEs defined in the same computational domain. Different (potentially non-nested) meshes can be used for the space discretization of the PDEs. The projection of the (primary) variables that are shared by the different PDEs (through the coupling terms) is carried out with Rescaled Localized Radial Basis Functions (RL-RBF). We validate our approach with a numerical test for which we also show the scalability of the intergrid transfer operator in the framework of high performance computing. Then, we apply it to the electromechanical model for the human heart function, and simulate a physiological heartbeat of an idealized left ventricle. We show that our approach enables the solution of large-scale multiphysics problems, especially when the individual models exhibit very different spatial scales. |
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33/2019 - 04/09/2019
Regazzoni, F.; Dede', L.; Quarteroni, A.
Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics | Abstract | | High fidelity (HF) mathematical models describing the generation of active force in the cardiac muscle tissue typically feature a large number of state variables to capture the intrinsically complex underlying subcellular mechanisms. With the aim of drastically reducing the computational burden associated with the numerical solution of these models, we propose a machine learning technique that builds a reduced order model (ROM). In our approach, the latter is obtained as the best-approximation of the HF model within a class of candidate models represented by means of Artificial Neural Networks (ANNs). The ANN is trained to learn the dynamics of the HF model from input-output pairs generated by the HF model itself from which the ROM is built in a non-intrusive (black-box) way. Moreover, the learning machine is informed with some a priori knowledge on the HF model, in a semi-physical (gray-box) way. A drastic reduction in both computational cost and memory storage is achieved with respect to the HF model. This is crucial when performing numerical simulations of the cardiac function, that is when active force models are exploited in the multiscale problem of cardiac electromechanics. As a matter of fact, we achieve a computational speedup of about one order of magnitude, while preserving almost the same accuracy of the HF solution. |
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35/2019 - 04/09/2019
Zancanaro, M.; Ballarin, F.; Perotto, S.; Rozza, G.
Hierarchical model reduction techniques for flow modeling in a parametrized setting | Abstract | | In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization, we consider two approaches, both based on a projection model reduction technique. The two methods differ for the algorithm employed during the construction of the reduced basis. In particular, the former employs the proper orthogonal decomposition, while the latter relies on a greedy algorithm according to the certified reduced basis technique. The two approaches are preliminarily compared on two-dimensional scalar and vector test cases. |
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34/2019 - 04/09/2019
Antonietti, P. F.; Mazzieri, I.; Melas, L.; Paolucci, R.; Quarteroni, A.; Smerzini, C.; Stupazzini, M.
Three-dimensional physics-based earthquake ground motion simulations for seismic risk assessment in densely populated urban areas | Abstract | | In this paper we introduce a mathematical and numerical approach aiming at coupling the physically simulated ground motion caused by earthquakes with empirical fragility functions introduced to model the structural damages induced to buildings. To simulate earthquake ground motion we solve a three-dimensional differential model at regional scale describing the propagation of seismic waves through the earth layers up to the surface, based on employing the discontinuous Galerkin spectral element method; selected intensity measure, retrieved from the synthetic time histories, are then employed as input for a vulnerability model based on fragility functions, in order to obtain a reliable prediction of buildings damage state.
The main features and effectiveness of the proposed numerical approach are tested on the Beijing metropolitan area (China). |
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32/2019 - 29/07/2019
Fedele, M.; Quarteroni, A.
Polygonal surface processing and mesh generation tools for numerical simulations of the complete cardiac function. | Abstract | | In order to simulate the cardiac function for a patient-specific geometry, the generation of the computational mesh is crucially important.
In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images.
These surfaces need ad-hoc processing to be suitable for a volumetric mesh generation.
In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process.
In particular, we focus on different aspects of a cardiac mesh generation pipeline:
a) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs;
b) generation of accurate boundary tags;
c) definition of mesh-size functions dependent on relevant geometric quantities;
d) processing and connecting together several volumetric meshes.
The new algorithms - implemented in the open-source software vmtk - can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled.
Thanks to these features, the proposed tools can significantly speed-up the mesh generation process for a large range of cardiac applications, from single-chamber single-physics simulations to multi-chambers multi-physics simulations.
We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.
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27/2019 - 11/07/2019
Tantardini, M.; Ieva, F.; Tajoli, L.; Piccardi, C.
Comparing methods for comparing networks | Abstract | | With the impressive growth of available data and the flexibility of network modelling, the problem of devising effective quantitative methods for the comparison of networks arises. Plenty of such methods have been designed to accomplish this task: most of them deal with undirected and unweighted networks only, but a few are capable of handling directed and/or weighted networks too, thus properly exploiting richer information. In this work, we contribute to the effort of comparing the different methods for comparing networks and providing a guide for the selection of an appropriate one. First, we review and classify a collection of
network comparison methods, highlighting the criteria they are based on and their advantages and drawbacks. Then, we test
the methods on synthetic networks and we asses their usability and the meaningfulness of the results they provide. Finally, we apply the methods to two real-world datasets, the European Air Transportation Network and the FAO Trade Network, in order to discuss the results that can be drawn from this type of analysis. |
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