MOX Reports
The preprint collection of the Laboratory for Modeling and Scientific Computation MOX. It mainly contains works on numerical
analysis and mathematical modeling applied to engineering problems. MOX web site is mox.polimi.it
Found 1287 products
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08/2021 - 02/13/2021
Antonietti, P. F.; Manuzzi, E.
Refinement of polygonal grids using Convolutional Neural Networks with applications to polygonal Discontinous Galerkin and Virtual Element methods | Abstract | | We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable refinement criteria to be possibly employed within adaptive refinement strategies. We propose two refinement strategies that exploit the use of CNNs to classify elements' shape, at a low computational cost. We test the proposed idea considering two families of finite element methods that support arbitrarily shaped polygonal elements, namely Polygonal Discontinuous Galerkin (PolyDG) methods and Virtual Element Methods (VEMs). We demonstrate that the proposed algorithms can greatly improve the performance of the discretization schemes both in terms of accuracy and quality of the underlying grids. Moreover, since the training phase is performed off-line and is problem independent the overall computational costs are kept low. |
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07/2021 - 02/13/2021
Diquigiovanni, J.; Fontana, M.; Vantini, S.
The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Data | Abstract | | Functional Data Analysis represents a field of growing interest in statistics. Despite
several studies have been proposed leading to fundamental results, the problem of
obtaining valid and efficient prediction sets has not been thoroughly covered. Indeed,
the great majority of methods currently in the literature rely on strong distributional
assumptions (e.g, Gaussianity), dimension reduction techniques and/or asymptotic
arguments. In this work, we propose a new nonparametric approach in the field of
Conformal Prediction based on a new family of nonconformity measures inducing
conformal predictors able to create closed-form finite-sample valid or exact prediction
sets under very minimal distributional assumptions. In addition, our proposal ensures
that the prediction sets obtained are bands, an essential feature in the functional
setting that allows the visualization and interpretation of such sets. The procedure is also fast, scalable, does not rely on functional dimension reduction techniques and allows the user to select different nonconformity measures depending on the problem at hand always obtaining valid bands. Within this family of measures, we propose also a specific measure leading to prediction bands asymptotically no less efficient than those obtained by not modulating. |
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06/2021 - 01/27/2021
Negrini, G.; Parolini, N.; Verani, M.
A diffuse interface box method for elliptic problems | Abstract | | We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori H1 and L2 error estimates highlighting the role of the mesh discretization parameter and of the diffuse interface width. Finally, we present a numerical result assessing the theoretical findings. |
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05/2021 - 01/25/2021
Antonietti, P.F.; Mazzieri, I.; Migliorini, F.
A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems | Abstract | | In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation.
By rewriting the original equation as a system of first order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable and retains super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two- and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical applications. |
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04/2021 - 01/25/2021
Orlando, V.; Rea, F.; Savaré, L.; Guarino, I; Mucherino, S.; Perrella, A.; Trama, U.; Coscioni, E.; Menditto, E.; Corrao, G.
Development and validation of a clinical risk score to predict the risk of SARS-CoV-2 infection from administrative data: A population-based cohort study from Italy | Abstract | | Background
The novel coronavirus (SARS-CoV-2) pandemic spread rapidly worldwide increasing exponentially in Italy. To date, there is lack of studies describing clinical characteristics of the people at high risk of infection. Hence, we aimed (i) to identify clinical predictors of SARSCoV-2 infection risk, (ii) to develop and validate a score predicting SARS-CoV-2 infection risk, and (iii) to compare it with unspecific scores.
Methods
Retrospective case-control study using administrative health-related database was carried
out in Southern Italy (Campania region) among beneficiaries of Regional Health Service aged over than 30 years. For each person with SARS-CoV-2 confirmed infection (case), up to five controls were randomly matched for gender, age and municipality of residence. Odds ratios and 90% confidence intervals for associations between candidate predictors and risk of infection were estimated by means of conditional logistic regression. SARS-CoV-2 Infection Score (SIS) was developed by generating a total aggregate score obtained from assignment of a weight at each selected covariate using coefficients estimated from the model. Finally, the score was categorized by assigning increasing values from 1 to 4. Discriminant power was used to compare SIS performance with that of other comorbidity scores.
Results
Subjects suffering from diabetes, anaemias, Parkinson’s disease, mental disorders, cardiovascular and inflammatory bowel and kidney diseases showed increased risk of SARSCoV-2 infection. Similar estimates were recorded for men and women and younger and older than 65 years. Fifteen conditions significantly contributed to the SIS. As SIS value increases, risk progressively increases, being odds of SARS-CoV-2 infection among people with the highest SIS value (SIS = 4) 1.74 times higher than those unaffected by any SIS contributing conditions (SIS = 1).
Conclusion
Conditions and diseases making people more vulnerable to SARS-CoV-2 infection were identified by the current study. Our results support decision-makers in identifying high-risk people and adopting of preventive measures to minimize the spread of further epidemic waves.
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03/2021 - 01/23/2021
Torti, A.; Marika, A.; Azzone, G.; Secchi, P.; Vantini S.
Bridge closure in the road network of Lombardy: a spatio-temporal analysis of the socio-economic impacts | Abstract | | This paper introduces a methodology to evaluate the socio-economic impacts of closure for maintenance of one or more infrastructures of a large and complex road network. Motivated by a collaboration with Regione Lombardia, we focus on a subset of bridges in the region, although we aim at developing a method scalable to all road infrastructures of the regional network, consisting of more than 10000 tunnels, bridges and overpasses. The final aim of the endeavor is to help decision-makers in prioritizing their interventions for maintaining and repairing infrastructure segments. We develop two different levels of impact assessment, both providing a unique global score for each bridge closure and investigating its spatio-temporal effects on mobility. We take advantage of a functional data analysis approach enhanced by a complex network theory perspective, thus modelling the roads of Lombardy as a network in which weights attributed to the edges are functional data. Results reveal the most critical bridges of Lombardy; moreover, for each bridge closure, the most impactful hours of the day and the most impacted municipalities of the region are identified. The proposed approach develops a flexible and scalable method for monitoring infrastructures of large and complex road networks.
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02/2021 - 01/23/2021
Calissano, A.; Feragen, A; Vantini, S.
Graph-Valued Regression: Prediction of unlabelled networks in a Non-Euclidean Graph-Space | Abstract | | Understanding how unlabeled graphs depend on input values or vectors is of extreme interest in a range of applications. In this paper, we propose a regression model taking values in Graph Space, representing unlabeled graphs which can be weighted or unweighted, one or multi-layer, and have same or different numbers of nodes, as a function of real valued regressor. As Graph Space is not a manifold, well-known manifold regression models are not applicable. We provide flexible parameterized regression models for Graph Space, along with precise and computationally efficient estimation procedures given by the introduced Align All and Compute regression algorithm. We show the potential of the proposed model for two real datasets: a time dependent cryptocurrency correlation matrices and a set of bus mobility usage network in Copenhagen (DK) during the Covid-19 pandemic. |
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01/2021 - 01/17/2021
Pegoraro, M.; Beraha, M.
Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric | Abstract | | We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line, with the 2-Wasserstein metric. We focus in particular on Principal Component Analysis (PCA) and regression. To define these models, we exploit a representation of the Wasserstein space closely related to its weak
Riemannian structure, by mapping the data to a suitable linear space and using a metric projection operator to constrain the results in the Wasserstein space. By carefully choosing the tangent point, we are able to derive fast empirical methods, exploiting a constrained B-spline approximation. As a byproduct of our approach, we are also able to derive faster routines for previous work on PCA for distributions. By means of simulation studies, we compare our approaches to previously proposed methods, showing that our projected PCA has similar performance for a fraction of the computational cost and that the projected regression is extremely flexible even under misspecification. Several theoretical properties of the models are investigated and asymptotic consistency is proven. Two real world applications to Covid-19 mortality in the US and wind speed forecasting are discussed.
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