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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77/2020 - 11/22/2020
Parolini, N.; Ardenghi, G.;Dede’, L.; Quarteroni, A.
A Mathematical Dashboard for the Analysis of Italian COVID-19 Epidemic Data | Abstract | | A data analysis of the COVID-19 epidemic is proposed on the basis of the dashboard publicly accessible at http://www.epimox.polimi.it that focuses on the characterization of the first and second epidemic outbreaks in Italy. The scope of this tool, which provides an immediate appreciation of the past epidemic development together with its current trends, is to foster a deeper interpretation of available data as well as to provide a hint on the near future evolution of the most relevant epidemic indicators. |
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75/2020 - 11/19/2020
F. Dassi; A. Fumagalli; D. Losapio; S. Scialò; A. Scotti; G. Vacca
The mixed virtual element method for grids with curved interfaces | Abstract | | In many applications the accurate representation of the computational domain is a key factor to obtain reliable and effective numerical solutions. Curved interfaces, which might be internal, related to physical data, or portions of the physical boundary, are often met in real applications. However, they are often approximated leading to a geometrical error that might become dominant and deteriorate the quality of the results. Underground problems often involve the motion of fluids where the fundamental governing equation is the Darcy law. High quality velocity fields are of paramount importance for the successful subsequent coupling with other physical phenomena such as transport. The virtual element method, as solution scheme, is known to be applicable in problems whose discretizations requires cells of general shape, and the mixed formulation is here preferred to obtain accurate velocity fields. To overcome the issues associated to the complex geometries and, at the same time, retaining the quality of the solutions, we present here the virtual element method to solve the Darcy problem, in mixed form, in presence of curved interfaces in two and three dimensions. The numerical scheme is presented in detail explaining the discrete setting with a focus on the treatment of curved interfaces. Examples, inspired from industrial applications, are presented showing the validity of the proposed approach. |
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76/2020 - 11/19/2020
Centofanti, F.; Lepore, A.; Menafoglio, A.; Palumbo, B.; Vantini, S.
Functional Regression Control Chart | Abstract | | The modern development of data acquisition technologies in many industrial processes is facilitating the collection of quality characteristics that are apt to be modelled as functions, which are usually referred to as pro les. At the same time, measurements of concurrent variables, which are related to the quality characteristic profiles, are often available in a functional form as well, and usually referred to as covariates. In order to adjust the monitoring of the quality characteristic pro les by the effect of this additional information, a new functional control chart is elaborated on the residuals obtained from a function-on-function linear regression of the quality characteristic profile on the functional covariates.
Furthermore, by means of a Monte Carlo simulation study, the performance of the proposed control chart are compared with those of other charts proposed in the literature. Eventually, a real-case study in the shipping industry is presented with the purpose of monitoring ship fuel consumption and thus, CO2 emissions from a Ro-Pax ship, with particular regard to detecting CO2 emission reduction after a specific energy efficiency initiative. |
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74/2020 - 11/09/2020
Formaggia, L; Fumagalli, A.; Scotti, A.
A multi-layer reactive transport model for fractured porous media | Abstract | | An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here the transported solute may precipitate and form a salt, or vice-versa. This phenomenon has been observed and reported in real outcrops. By changing its physical properties this layer might substantially alter the global flow response of the system and thus the actual transport of solute: the problem is thus non-linear and fully coupled. The aim of this work is to propose a new mathematical model for reactive flow in fractured porous media, by approximating both the fracture and these surrounding layers via a reduced model. In particular, our main goal is to describe the layer thickness evolution with a new mathematical model, and compare it to a fully resolved equidimensional model for validation. As concerns numerical approximation we extend an operator splitting scheme in time to solve sequentially, at each time step, each physical process thus avoiding the need for a non-linear monolithic solver, which might be challenging due to the non-smoothness of the reaction rate. We consider bi- and tridimensional numerical test cases to asses the accuracy and benefit of the proposed model in realistic scenarios. |
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73/2020 - 11/07/2020
Bennati, L.; Vergara, C.; Domanin, M.; Trimarchi, S.; Malloggi, C.; Silani, V.; Parati, G.; Casana, R.
A computational fluid structure interaction study for carotids with different atherosclerotic plaques | Abstract | | Atherosclerosis is a systemic disease that leads to accumulation of deposits, known as atherosclerotic plaques, within the walls of the carotids. In particular, three types of plaque can be distinguished: soft, fibrous and calcific. Most of the computational studies who investigated the interplay between the plaque and the blood flow on patient-specific geometries, used non standard medical images to directly delineate and segment the plaque and its components. However these techniques are not so widely available in the clinical practice. In this context the aim of our work was twofold: i) to propose a new geometric tool that allowed to reconstruct a plausible plaque in the carotids from standard images and ii) to perform 3D FSI simulations where we compared some fluid-dynamic and structural quantities among 15 patients characterized by different typologies of plaque. Our results highlighted that both the morphology and the mechanical properties of different plaque components play a crucial role in determining the vulnerability of the plaque. |
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72/2020 - 11/07/2020
Belli E.; Vantini S.
Measure Inducing Classification and Regression Trees for Functional Data | Abstract | | We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing generalization error while retaining the interpretability of a tree. This is achieved by learning a weighted functional L2 space by means of constrained convex optimization, which is then used to extract multiple weighted integral features from the input functions, in order to determine the binary split for each internal node of the tree. The approach is designed to manage multiple functional inputs and/or outputs, by defining suitable splitting rules and loss functions that can depend on the specific problem and can also be combined with scalar and categorical data, as the tree is grown with the original greedy CART algorithm. We focus on the case of scalar-valued functional inputs defined on unidimensional domains and illustrate the effectiveness of our method in both classification and regression tasks, through a simulation study and four real world applications. |
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71/2020 - 11/07/2020
Belli E; Vantini S.
Ridge regression with adaptive additive rectangles and other piecewise functional templates | Abstract | | We propose an L2-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template ?, which is constrained to belong to a class of piecewise functions by restricting its basis expansion. In particular, we focus on the case where ? can be expressed as a sum of q rectangles that are adaptively positioned with respect to the regression error. As the problem of finding the optimal knot placement of a piecewise function is nonconvex, the proposed parametrization allows to reduce the number of variables in the global optimization scheme, resulting in a fitting algorithm that alternates between approximating a suitable template and solving a convex ridge-like problem. The predictive power and interpretability of our method is shown on multiple simulations and two real world case studies. |
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70/2020 - 11/07/2020
Belli E.
Smoothly Adaptively Centered Ridge Estimator | Abstract | | With a focus on linear models with smooth functional covariates, we propose a penalization framework (SACR) based on the nonzero centered ridge, where the center of the penalty is optimally reweighted in a supervised way, starting from the ordinary ridge solution as the initial centerfunction. In particular, we introduce a convex formulation that jointly estimates the model's coefficients and the weight function, with a roughness penalty on the centerfunction and constraints on the weights in order to recover a possibly smooth and/or sparse solution. This allows for a non-iterative and continuous variable selection mechanism, as the weight function can either inflate or deflate the initial center, in order to target the penalty towards a suitable center, with the objective to reduce the unwanted shrinkage on the nonzero coefficients, instead of uniformly shrinking the whole coefficient function. As empirical evidence of the interpretability and predictive power of our method, we provide a simulation study and two real world spectroscopy applications with both classification and regression. |
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