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 1349 prodotti
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25/2020 - 16/04/2020
Calvetti, D.; Cosmo, A.; Perotto, S.; Somersalo, E.
Bayesian mesh adaptation for estimating distributed parameters | Abstract | | The problem of estimating numerically a distributed parameter from indirect measurements arises in many applications, and in that context the choice of the discretization plays an important role. In fact, to guarantee a certain level of accuracy of the forward model that maps the unknown to the observations may require a fine discretization, adding to the complexity of the problem and to the computational cost. On the other hand, reducing the complexity of the problem by adopting a coarser discretization may increase the modeling error and can be very detrimental for ill-posed inverse problems. To balance accuracy and complexity, we propose an adaptive algorithm for adjusting the discretization level automatically and dynamically while estimating the unknown distributed parameter by an iterative scheme. In the Bayesian paradigm, all unknowns, including the metric that defines the discretization, are modeled as random variables. Our approach couples the discretization with a Bayesian hierarchical hyperparameter that is estimated simultaneously with the unknown parameter of primary interest. The viability of the proposed algorithm, the Bayesian Mesh Adaptation (BMA) is assessed on two test cases, a fan-beam X-ray tomography and an inverse source problem for a Darcy flow model. |
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24/2020 - 16/04/2020
Formaggia, L.; Scotti, A.; Fumagalli, A.
Numerical Methods for Flow in Fractured Porous Media | Abstract | | In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the latter, we discuss strategies that are developed in literature for its numerical solution mainly related to the geometrical relation between the fractures and porous media grids. |
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23/2020 - 16/04/2020
Spreafico, M.; Ieva, F.
Functional modelling of recurrent events on time-to-event processes | Abstract | | In clinical practice many situations can be modelled in the framework of recurrent events. It is often the case where the association between the occurrence of events and time-to-event outcomes is of interest. The purpose of our study is to enrich the information available for modelling survival with relevant dynamic features, properly taking into account their possibly time-varying nature, as well as to provide a new setting for quantifying the association between time-varying processes and time-to-event outcomes. We propose an innovative methodology to model information carried out by time-varying processes by means of functional data. The main novelty we introduce consists in modelling each time-varying variable as the compensator of marked point process the recurrent events are supposed to derive from. By means of Functional Principal Component Analysis (FPCA), a suitable dimensional reduction of these objects is carried out in order to plug them into a survival Cox regression model. We applied our methodology to data retrieved from the administrative databases of Lombardy Region (Italy), related to patients hospitalized for Heart Failure (HF) between 2000 and 2012. We focused on time-varying processes of HF hospitalizations and multiple drugs consumption and we studied how they influence patients’ long-term survival. The introduction of this novel way to account for time-varying variables allowed for modelling self-exciting behaviours, for which the occurrence of events in the past increases the probability of a new event, and to make personalized predictions, quantifying the effect of personal behaviours and therapeutic patterns on survival. |
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22/2020 - 16/04/2020
Zeni, G.; Fontana, M.; Vantini, F.
Conformal Prediction: a Unified Review of Theory and New Challenges | Abstract | | In this work we provide a review of basic ideas and novel developments about Conformal Prediction - an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions - that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case.
The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.
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21/2020 - 16/04/2020
Benacchio, T.; Bonaventura, L.; Altenbernd, M.; Cantwell, C.D.; Düben, P.D.; Gillard, M.; Giraud, L.; Göddeke, D.; Raffin, E.; Teranishi, K.; Wedi, N.
Resilience and fault-tolerance in high-performance computing for numerical weather and climate prediction | Abstract | | Numerical weather and climate prediction rates as one of the scientific applications whose accuracy improvements greatly depend on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increasing average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys approaches for fault-tolerance in numerical algorithms and system resilience in parallel simulations from the perspective of numerical weather and climate prediction systems. A selection of existing strategies is analyzed, featuring interpolation-restart and compressed checkpointing for the numerics, in-memory checkpointing, ULFM- and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analyzed and some recommendations outlined for future developments. |
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20/2020 - 16/04/2020
Almi, S.; Belz, S.; Micheletti, S.; Perotto, S.
A DIMENSION-REDUCTION MODEL FOR BRITTLE FRACTURES ON THIN SHELLS WITH MESH ADAPTIVITY | Abstract | | In this paper we derive a new two-dimensional brittle fracture
model for thin shells via dimension reduction, where the admissible displacements
are only normal to the shell surface. The main steps include to endow
the shell with a small thickness, to express the three-dimensional energy in
terms of the variational model of brittle fracture in linear elasticity, and to
study the ????-limit of the functional as the thickness tends to zero.
The numerical discretization is tackled by first approximating the fracture
through a phase field, following an Ambrosio-Tortorelli like approach, and then
resorting to an alternating minimization procedure, where the irreversibility
of the crack propagation is rigorously imposed via an inequality constraint.
The minimization is enriched with an anisotropic mesh adaptation driven by
an a posteriori error estimator, which allows us to sharply track the whole
crack path by optimizing the shape, the size, and the orientation of the mesh
elements.
Finally, the overall algorithm is successfully assessed on two Riemannian
settings and proves not to bias the crack propagation. |
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19/2020 - 12/03/2020
Stella, S.; Vergara, C.; Maines, M.; Catanzariti, D.; Africa, P.; Demattè, C.; Centonze, M.; Nobile, F.; Del Greco, M.; Quarteroni, A.
Integration of maps of activation times in computational cardiac electrophysiology | Abstract | | In this work we used the monodomain equation
in combination with the Bueno-Orovio ionic model for the prediction of the activation
times in cardiac electro-physiology. We considered four patients who suffered from Left
Bundle Branch Block (LBBB) and patient-specific maps of activation times obtained by inserting in the ventricles
electrodes located on catheters. We used activation maps acquired at the septum as input data for the model
and maps at the epicardial veins for the validation of the monodomain model
in the context of a normal excitation. In particular, a first set (half) of the latter
were used to estimate the conductivities of the patient and a second set (the remaining half) to compute
the errors of the numerical simulations. We found an excellent agreement between measures and numerical
results. Our validated
computational tool could be used to accurately predict activation times at the epicardial veins,
allowing to shorten the mapping procedure and reduce the exposition to radiations.
This could be of great interest for clinical applications, for example in the Cardiac Resynchronization
Therapy (CRT) where such mapping is commonly used to determine the best point of stimulus. |
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16/2020 - 05/03/2020
Paolucci, R.; Mazzieri, I.; Piunno, G.; Smerzini, C.; Vanini, M.; Ozcebe, A.G.
Earthquake ground motion modelling of induced seismicity in the Groningen gas field | Abstract | | A key element in the seismic hazard and risk assessment due to induced earthquakes in the Groningen gas field is a
ground motion model (GMM). Although significant efforts have been devoted to the construction of an empirical
GMM, there is a growing interest in reducing its uncertainty through data-driven approaches. In the framework of
the KEM research program launched by the Ministry of Economic Affairs and Climate Policy of the Netherlands,
the authors explored the use of 3D physics-based numerical approaches to characterize earthquake ground motion in
the Groningen area and to shed light on the potential impact of the specific geologic conditions, characterized by
irregular geologic interfaces and thick layers of soft deposits at ground surface. Within the wider scope of this
research, this paper is focused on the construction and validation of a large-scale ( 20 km × 20 km), heterogeneous
3D seismic wave propagation model for the Groningen area, based on the significant bulk of available geological,
geophysical, geotechnical and seismological data.
Results of physics-based numerical simulations are validated against the ground motion recordings of the Jan 8,
2018, ML 3.4 Zeerijp earthquake – the third largest event to date in the area. Taking advantage of suitable models of
slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found
to reproduce accurately the observed features of ground motions at short epicentral distance (Repi < 10 km), in a
broad frequency range, up to about 10 Hz. To achieve this level of accuracy, the total number of degrees-of-freedom
was up to about 1 billion, implying taking advantage of high performance computing facilities. A sensitivity analysis
is also addressed to discuss the impact of key modeling assumptions, specifically, the role of 3D underground
geological features (“tunnel valleys”), the stochastic variability of shallow seismic velocities and the amplitude and
frequency dependence of the quality factor. Amongst others, results point out crucial aspects in deriving GMMs for
induced seismicity in Groningen, such as the magnitude and distance dependence of site amplification functions
associated with 3D wave propagation features, as opposed to the standard assumption of vertically propagating
plane waves. |
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