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 1268 prodotti
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36/2021 - 11/06/2021
Parolini, N.; Dede', L; Antonietti, P. F.; Ardenghi, G.; Manzoni, A.; Miglio, E.; Pugliese, A.; Verani, M.; Quarteroni, A.
SUIHTER: A new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy | Abstract | | The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated infected (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of reproducing the past history of the epidemic in Italy, surfaced in late February and still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are daily made available from the Italian Civil Protection. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak emerged in Fall 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at national level. |
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38/2021 - 11/06/2021
Giusteri, G. G.; Miglio, E.; Parolini, N.; Penati, M.; Zambetti, R.
Simulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strands | Abstract | | We propose a method for the description and simulation of the nonlinear dynamics of slender structures modeled as Cosserat rods. It is based on interpreting the strains and the generalized velocities of the cross sections as basic variables and elements of the special Euclidean algebra. This perspective emerges naturally from the evolution equations for strands, that are one-dimensional submanifolds, of the special Euclidean group. The discretization of the corresponding equations for the three-dimensional motion of a Cosserat rod is performed, in space, by using a staggered grid. The time evolution is then approximated with a semi-implicit method. Within this approach we can easily include dissipative effects due to both the action of external forces and the presence of internal mechanical dissipation. The comparison with results obtained with different schemes shows the effectiveness of the proposed method, which is able to provide very good predictions of nonlinear dynamical effects and shows competitive computation times also as an energy-minimizing method to treat static problems. |
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35/2021 - 04/06/2021
Regazzoni, F.; Quarteroni, A.
Accelerating the convergence to a limit cycle in 3D cardiac electromechanical simulations through a data-driven 0D emulator | Abstract | | The results of numerical simulations of 3D cardiac electromechanical models are typically characterized by a long transient before reaching a periodic solution known as limit cycle. Since the only clinically relevant output is the one associated with such limit cycle, a long transient translates into a serious computational overhead. To accelerate the convergence to the limit cycle, we propose a strategy based on a surrogate model, wherein the computationally demanding 3D components are replaced by a 0D emulator. This emulator is built through an automated data-driven algorithm on the basis of pressure-volume transients of as few as three heartbeats simulated through the 3D model. The 0D emulator, consisting of a time-dependent pressure-volume relationship, allows to accurately detect the location of the limit cycle in less than one minute on a standard laptop. Then, using as an initial guess for the 3D model the solution obtained with its 0D surrogate, it is possible to reach in just two heartbeats a solution that is as close to the limit cycle as the one obtained after more than 20 heartbeats with the full-order 3D model. In this manner, the proposed approach achieves an overall speedup in the simulation of about an order of magnitude.
In practical applications, an electromechanical model needs to be coupled with a model for the external circulation. The latter is typically represented by either a Windkessel-type preload-afterload model, emulating the boundary conditions, or by a closed-loop model of the entire circulatory network. The closed-loop model provides higher quality results in terms of physiological soundness; however, reaching a limit cycle is more challenging in this setting. It is in this context that our 0D emulator turns out to be particularly effective.
The 0D emulator is also recommended in many-query settings (e.g. when performing sensitivity analysis, parameter estimation and uncertainty quantification), that call for the repeated solution of the model for different values of the parameters. As a matter of fact, the emulator does not depend on the circulation model to which it is coupled, hence its construction does not have to be repeated when the parameters of the circulation model vary. Finally, should the parameters of the 3D electromechanical model vary as well, we propose a parametric emulator, obtained by interpolation of emulators constructed for given values of the parameters. In all these cases, our numerical results show that the emulator is able to provide the 3D model with an initial guess such that, after only two heartbeats, the solution is very close to the limit cycle. This paper is accompanied by a Python library implementing the proposed algorithm, open to the integration with existing cardiac solvers. |
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34/2021 - 04/06/2021
Bonaventura, L.; Gatti F.; Menafoglio A.; Rossi D.; Brambilla D.; Papini M.; Longoni L.
An efficient and robust soil erosion model at the basin scale | Abstract | | We present a numerical model of soil erosion at the basin scale that allows one to describe surface run-off without a priori identifying drainage zones, river beds and other water bodies. The model is based on robust and unconditionally stable numerical techniques and guarantees
mass conservation and positivity of the surface and subsurface water layers. Furthermore, the method is equipped with a geostatistical preprocessor that can perform downscaling of data retrieved from digital databases at coarser resolutions and integrate them with
field measurements. Numerical experiments on both idealized and realistic configurations demonstrate the
effectiveness of the proposed method in reproducing transient high resolution features at a reduced computational cost and to reproduce correctly the main hydrographic features of the considered catchment. Furthermore, probabilistic forecasts can
be carried out, also with limited computational effort, based on soil data automatically generated by the geostatistical preprocessor. Even though the model results are still far from full quantitative agreement with the available data, robust estimates of water levels, discharge and of the order of magnitude of the total sediment yield were achieved in two validation experiments on realistic benchmarks. |
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33/2021 - 02/06/2021
Lupo Pasini, M.; Gabbi, V.; Yin, J.; Perotto, S.; Laanait, N.
Scalable balanced training of conditional generative adversarial neural networks on image data | Abstract | | We propose a distributed approach to train deep convolutional generative adversarial neural network (DC-CGANs) models. Our method reduces the imbalance between generator and discriminator by partitioning the training data according to data labels, and enhances scalability by performing a parallel training where multiple generators are concurrently trained, each one of them focusing on a single data label. Performance is assessed in terms of inception score and image quality on MNIST, CIFAR10, CIFAR100, and ImageNet1k datasets, showing a significant improvement in comparison to state-of-the-art techniques to training DC-CGANs.
Weak scaling is attained on all the four datasets using up to 1,000 processes and 2,000 NVIDIA V100 GPUs on the OLCF supercomputer Summit. |
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32/2021 - 02/06/2021
Sangalli, L.M.
Spatial regression with partial differential equation regularization | Abstract | | This work gives an overview of an innovative class of methods for the analysis of spatial and of functional data observed over complicated two-dimensional domains. This class is based on regression with regularizing terms involving partial differential equations. The associated estimation problems are solved resorting to advanced numerical analysis techniques. The synergical interplay of approaches from statistics, applied mathematics and engineering endows the methods with important advantages with respect to the available techniques, and makes them able to accurately deal with data structures for which the classical techniques are unfit. Spatial regression with differential regularization is illustrated via applications to the analysis of eco-color doppler measurements of blood-flow velocity, and to functional magnetic resonance imaging signals associated with neural connectivity in the cerebral cortex. |
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31/2021 - 02/06/2021
Ferraccioli, F.; Arnone, E.; Finos, L.; Ramsay, J.O.; Sangalli, L.M.
Nonparametric density estimation over complicated domains | Abstract | | We propose a nonparametric method for density estimation over
(possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a di fferential operator. We demonstrate the good inferential properties of the method.
Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements.
This ensures high computational efficiency and enables great
flexibility. The proposed method efficiently deals with data scattered over regions having complicated shapes, featuring complex boundaries, sharp
concavities or holes. Moreover, it captures very well complicated signals having multiple modes with di fferent directions and intensities of anisotropy. We show the comparative advantages of the proposed approach over state of the art methods, in simulation studies and in an
application to the study of criminality in the city of Portland, Oregon. |
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30/2021 - 01/06/2021
Fumagalli, I.
A reduced 3D-0D FSI model of the aortic valve including leaflets curvature | Abstract | | In the present work, we propose a novel lumped-parameter model for
the description of the aortic valve dynamics, including elastic effects associated to the leaflets’ curvature. The introduction of a lumped-parameter model based on momentum balance entails an easier calibration of the parameter models, that are instead typically numerous in phenomenologicalbased models. This model is coupled with 3D Navier-Stokes equations describing the blood flow, where the valve surface is represented by a resistive method, and valve leaflets velocity is taken into consideration.
The resulting reduced fluid-structure interaction problem has a computational cost that is comparable with the solution of a prescribed-motion fluid dynamics problem. A SUPG-PSPG stabilized finite element scheme is adopted for the discretization of the coupled problem, and the computational results show the suitability of the system in representing the leaflets motion, the blood flow in the ascending aorta, and the pressure jump across the leaflets. |
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