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 1242 prodotti
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41/2019 - 09/11/2019
Abbà, A.; Bonaventura, L.; Recanati, A.; Tugnoli, M.;
Dynamical p-adaptivity for LES of compressible flows in a high order DG framework | Abstract | | We investigate the possibility of reducing the computational burden of LES models by employing locally and dynamically adaptive polynomial degrees in the framework of a high order DG method. A degree adaptation technique especially featured to be effective for LES applications, that was previously developed by the authors and tested in the statically adaptive case, is applied here in a dynamically adaptive fashion.
Two significant benchmarks are considered, comparing the results of adaptive and non adaptive simulations.
The proposed dynamically adaptive approach allows for a significant reduction of the computational cost of representative LES computation, while allowing to maintain the level of accuracy guaranteed by LES carried out with constant, maximum polynomial degree values. |
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38/2019 - 16/10/2019
Massi, M.C.; Ieva, F.; Gasperoni, F.; Paganoni, A.M.
Minority Class Feature Selection through Semi-Supervised Deep Sparse Autoencoders | Abstract | | Class imbalance is a common issue in many domain applications of learning algorithms. Oftentimes, in the same domains it is much more relevant to correctly classify and profile minority class examples
with respect to majority class ones. To solve classification problems in imbalanced settings, and improve accuracy specifically on the minority class, we propose a feature selection algorithm based on the
application of a Deep Sparse AutoEncoder (DSAE) as a semi-supervised outlier detection method, where minority class examples are considered outliers of the normal population of majority class observations. We use a DSAE trained only on normal observations to reconstruct both inliers and outliers. From the analysis of the Reconstruction Error (RE) on both classes, we determine in which features the minority class has a significantly different distribution of values with respect to the majority class, thus identifying the most relevant features to discriminate between the two classes. We proved the efficacy of our algorithm in improving minority class classification accuracy (evaluated on specificity and AUROC metrics) on different datasets of high dimensionality and varying sample size, outperforming other benchmark feature selection methods. |
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40/2019 - 16/10/2019
Lovato, I.; Pini, A.; Stamm, A.; Vantini, S.
Model-free two-sample test for network-valued data | Abstract | | In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In details, the present framework proceeds in four steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the {R} package texttt{nevada} (NEtwork-VAlued Data Analysis). |
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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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