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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27/2020 - 05/08/2020
Spreafico, M.; Ieva, F.; Fiocco, M.
Modelling dynamic covariates effect on survival via Functional Data Analysis: application to the MRC BO06 trial in osteosarcoma | Abstract | | Time-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions of time and chemotherapy treatment is modified by delaying a course or reducing the dose intensity, according to patient’s toxicity levels. Models for time-to-event to deal with the dynamic nature of time-varying covariates during follow-up are necessary, still not well developed. In this work, innovative methods to represent time-dependent covariates by means of Functional Data Analysis (FDA) and how to include them into survival models are discussed. This new approach was applied to osteosarcoma data from the MRC BO06/EORTC 80931 randomized clinical trial, new insights into the clinical research. Time-varying covariates related to alkaline phosphatase (ALP) and chemotherapy dose during treatment were considered. Processes dynamics over time were investigated and additional information that may be related to the survival were included into the time-to-event models. High ALP levels reflected poor overall survival. Although dose-intense profiles were not associated with a better survival, the strength of our method is the ability to detect differences between patients with different biomarker evolution and treatment response, even when randomised to the same regimen. This aspect is seldom addressed in the literature. |
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26/2020 - 05/08/2020
Zonca, S.; Antonietti, P.F.; Vergara, C.
A Polygonal Discontinuous Galerkin formulation for contact mechanics in fluid-structure interaction problems | Abstract | | In this work, we propose a formulation based on the Polygonal Discontinuous Galerkin (PolyDG) method for contact mechanics that arises in fluid-structure interaction problems. In particular, we introduce a consistent penalization approach to treat the frictionless contact between immersed structures that undergo large displacements. The key feature of the method is that the contact condition can be naturally embedded in the PolyDG formulation, allowing to easily support polygonal/polyhedral meshes. The proposed approach introduced a fixed background mesh for the fluid problem overlapped by the structure grid that is able to move independently of the fluid one. To assess the validity of the proposed approach, we report the results of several numerical experiments obtained in the case of contact between flexible structures immersed in a fluid. |
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25/2020 - 04/16/2020
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 - 04/16/2020
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 - 04/16/2020
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 - 04/16/2020
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 - 04/16/2020
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 - 04/16/2020
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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