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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59/2020 - 07/08/2020
Massi, M.C.; Franco, N.R; Ieva, F.; Manzoni, A.; Paganoni, A.M.; Zunino, P.
High-Order Interaction Learning via Targeted Pattern Search | Abstract | | Logistic Regression (LR) is a widely used statistical method in empirical studies in many research fields. However, these real-life scenarios oftentimes share complexities that would hinder the application of the as-is model. First and foremost, the need to include high-order interactions to capture the variability of their data. Moreover, these studies are seldom developed in imbalanced settings, with datasets growing wider, sample size
from very large to extremely small and a strong need for model and results interpretability.
In this paper we present a novel algorithm, High-Order Interaction Learning via targeted Pattern search (HOILP), to select interaction terms of varying order to include in a LR for
an imbalanced binary classification task when input data is categorical. HOILP’s rationale is built on the duality between item sets and categorical interactions, and is composed of
(i) an interaction learning step based on a well-known frequent item set mining algorithm and (ii) a novel dissimilarity-based interaction selection step, that allows the user to control
for the number of interactions to include in the LR model. Besides HOILP we present here two variants (Scores HOILP and Clusters HOILP), that can suit even more specific needs.
Through a set of experiments we validate our algorithm and prove its wide applicability to real-life research scenarios, surpassing the performance of a benchmark state-of-the-art
algorithm. |
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58/2020 - 07/08/2020
Beraha, M.; Pegoraro, M.; Peli, R.; Guglielmi, A
Spatially dependent mixture models via the Logistic Multivariate CAR prior | Abstract | | We consider the problem of spatially dependent areal data, where for each
area independent observations are available, and propose to model
the density of each area through a finite mixture of Gaussian distributions.
The spatial dependence is introduced via a novel joint distribution for
a collection of vectors in the simplex, that we term logisticMCAR.
We show that salient features of the logisticMCAR distribution
can be described analytically, and that a suitable augmentation scheme based on the
P{'o}lya-Gamma identity allows to derive an efficient Markov Chain Monte Carlo
algorithm.
When compared to competitors, our model has proved to better estimate densities in different (disconnected) areal locations when they have different characteristics.
We discuss an application on a real dataset of Airbnb listings in the city
of Amsterdam, also showing how to easily incorporate for additional covariate
information in the model. |
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57/2020 - 07/08/2020
Regazzoni, F.; Quarteroni, A.
An oscillation-free fully partitioned scheme for the numerical modeling of cardiac active mechanics | Abstract | | In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For the numerical solution of the coupled model, partitioned schemes, that foresee the sequential solution of the two subproblems, are often used. However, this approach may be unstable. For this reason, the coupled model is commonly solved as a unique system using Newton type algorithms, at the price, however, of high computational costs. In light of this motivation, in this paper we propose a new numerical scheme, that is numerically stable and accurate, yet within a fully partitioned (i.e. segregated) framework. Specifically, we introduce, with respect to standard segregated scheme, a numerically consistent stabilization term, capable of removing the nonphysical oscillations otherwise present in the numerical solution of the commonly used segregated scheme. Our new method is derived moving from a physics-based analysis on the microscale energetics of the force generation dynamics. By considering a model problem of active mechanics we prove that the proposed scheme is unconditionally absolutely stable (i.e. it is stable for any time step size), unlike the standard segregated scheme, and we also provide an interpretation of the scheme as a fractional step method. We show, by means of several numerical tests, that the proposed stabilization term successfully removes the nonphysical numerical oscillations characterizing the non stabilized segregated scheme solution. Our numerical tests are carried out for several force generation models available in the literature, namely the Niederer-Hunter-Smith model, the model by Land and coworkers, and the mean-field force generation model that we have recently proposed. Finally, we apply the proposed scheme in the context of a three-dimensional multiscale electromechanical simulation of the left ventricle. |
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56/2020 - 07/08/2020
Botti, L.; Botti, M.; Di Pietro, D. A.;
A Hybrid High-Order method for multiple-network poroelasticity | Abstract | | We develop Hybrid High-Order methods for multiple-network poroelasticity, modelling seepage through deformable fissured porous media. The proposed methods are designed to support general polygonal and polyhedral elements. This is a crucial feature in geological modelling, where the need for general elements arises, e.g., due to the presence of fracture and faults, to the onset of degenerate elements to account for compaction or erosion, or when nonconforming mesh adaptation is performed. We use as a starting point a mixed weak formulation where an additional total pressure variable is added, that ensures the fulfilment of a discrete inf-sup condition. A complete theoretical analysis is performed, and the results are demonstrated on a panel of numerical tests. |
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55/2020 - 07/08/2020
Botti, M.; Castanon Quiroz, D.; Di Pietro, D.A.; Harnist, A.
A Hybrid High-Order method for creeping flows of non-Newtonian fluids | Abstract | | In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray--Lions scalar problems.
A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau--Yasuda models. Numerical examples complete the exposition. |
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54/2020 - 23/07/2020
Arnone, E.; Bernardi, M. S.; Sangalli, L. M.; Secchi, P.
Analysis of Telecom Italia mobile phone data by space-time regression with differential regularization | Abstract | | We apply spatio-temporal regression with partial differential equation regularization to the Telecom Italia mobile phone data. The technique proposed allows to include specific information on the phenomenon under study through a definition of the non-stationary anisotropy characterizing the spatial regularization based on the texture of the domain on which the data are observed. |
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53/2020 - 23/07/2020
Arnone, E.; Kneip, A.; Nobile, F.; Sangalli, L. M.
Some numerical test on the convergence rates of regression with differential regularization | Abstract | | We numerically study the bias and the mean square error of the estimator in Spatial Regression with Partial Differential Equation (SR-PDE) regularization.
SR-PDE is a novel smoothing technique for data distributed over two-dimensional domains, which allows to incorporate prior information formalized in term of a partial differential equation. This technique also enables an accurate estimation when the shape of the domain is complex and it strongly influences the phenomenon under study. |
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52/2020 - 23/07/2020
Arnone, E.; Kneip, A.; Nobile, F.; Sangalli, L. M.
Some first results on the consistency of spatial regression with partial differential equation regularization | Abstract | | We study the consistency of the estimator in spatial regression with partial differential equation (PDE) regularization. This new smoothing technique allows to accurately estimate spatial fields over complex two-dimensional domains, starting from noisy observations; the regularizing term involves a PDE that formalizes problem specific information about the phenomenon at hand. Differently from classical smoothing methods, the solution of the infinite-dimensional estimation
problem cannot be computed analytically. An approximation is obtained via the finite element method, considering a suitable triangulation of the spatial domain. We first consider the consistency of the estimator in the infinite-dimensional setting. We then study the consistency of the finite element estimator, resulting from the approximated PDE. We study the bias and variance of the estimators, with respect to the sample size and to the value of the smoothing parameter. Some final
simulation studies provide numerical evidence of the rates derived for the bias, variance and mean square error. |
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