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 1239 products
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81/2022 - 11/28/2022
Bonizzoni, F.; Hauck, M.; Peterseim, D.
A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems | Abstract | | This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines the reduced basis (RB) framework with the recently proposed super-localized orthogonal decomposition (SLOD). More specifically, the RB is used for accelerating the typically costly SLOD basis computation, while the SLOD is employed for an efficient compression of the problem's solution operator requiring coarse solves only. The combined advantages of both methods allow one to tackle the challenges arising from parametric heterogeneous
coefficients. Given a value of the parameter vector, the method outputs a corresponding compressed solution operator which can be used to efficiently treat multiple, possibly non-affine, right-hand sides at the same time, requiring only one coarse solve per right-hand side. |
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80/2022 - 11/09/2022
Balduzzi, G.; Bonizzoni, F.; Tamellini, L.
Uncertainty quantification in timber-like beams using sparse grids: theory and examples with off-the-shelf software utilization | Abstract | | When dealing with timber structures, the characteristic strength and stiffness of the material are made highly variable and uncertain by the unavoidable, yet hardly predictable, presence of knots and other defects. In this work we apply the sparse grids stochastic collocation method to perform uncertainty quantification for structural engineering in the scenario
described above. Sparse grids have been developed by the mathematical community in the last decades and their theoretical background has been rigorously and extensively studied. The document proposes a brief practice-oriented introduction with minimal theoretical background, provides detailed instructions for the use of the already implemented Sparse Grid Matlab kit (freely available on-line) and discusses two numerical examples inspired from timber engineering problems that highlight how sparse grids exhibit superior performances compared to the plain Monte Carlo method. The Sparse Grid Matlab kit requires only a few lines of code to be interfaced with any numerical solver for mechanical problems (in this work we used an isogeometric collocation method) and provides outputs that can be easily interpreted and used in the engineering practice. |
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79/2022 - 11/04/2022
Antonietti, P. F.; Farenga, N.; Manuzzi, E.; Martinelli, G.; Saverio, L.
Agglomeration of Polygonal Grids using Graph Neural Networks with applications to Multigrid solvers | Abstract | | Agglomeration-based strategies are important both within adaptive refinement algorithms and to construct scalable multilevel algebraic solvers. In order to automatically perform agglomeration of polygonal grids, we propose the use of Graph Neural Networks (GNNs) to partition the connectivity graph of a computational mesh. GNNs have the advantage to process naturally and simultaneously both the graph structure of mesh and the geometrical information, such as the areas of the elements or their barycentric coordinates. This is not the case with other approaches such as METIS, a standard algorithm for graph partitioning which is meant to process only the graph information, or the k-means clustering algorithm, which can process only the geometrical information. Performance in terms of quality metrics is enhanced for Machine Learning (ML) strategies, with GNNs featuring a lower computational cost online. Such models also show a good degree of generalization when applied to more complex geometries, such as brain MRI scans, and the capability of preserving the quality of the grid. The effectiveness of these strategies is demonstrated also when applied to MultiGrid (MG) solvers in a Polygonal Discontinuous Galerkin (PolyDG) framework. |
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78/2022 - 11/04/2022
Bucelli, M.; Gabriel, M. G.; Gigante, G.; Quarteroni, A.; Vergara, C.
A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction | Abstract | | We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the different submodels. Our scheme relies on a segregated treatment of the subproblems, in particular on an explicit Robin-Neumann algorithm for the fluid-structure interaction, aiming at reducing the computational burden of numerical simulations. The results, both in an ideal and a realistic cardiac setting, show that the proposed scheme is stable at the regimes typical of cardiac simulations. From a comparison with a scheme with implicit fluid-structure interaction, it emerges that, while conservation properties are not fully preserved, computational times significantly benefit from the explicit scheme. Overall, the explicit discretization represents a good trade-off between accuracy and cost, and is a valuable alternative to implicit schemes for fast large-scale simulations. |
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77/2022 - 10/31/2022
Ziarelli, G.; Dede', L.; Parolini, N.; Verani, M.; Quarteroni, A.
Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: an application to the Italian scenario. | Abstract | | In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory can be a useful tool based on solid mathematical bases to plan the vaccination campaign in the direction of eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a fixed time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Overall, we formalize an optimal control framework adopting the model as state problem by acting on the administrations of vaccine-doses. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, shows that the presented framework can be a valuable tool to support the planning of vaccination campaigns minimizing specific goals. |
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76/2022 - 10/25/2022
Spreafico, M.; Ieva, F.; Fiocco, M.
Longitudinal Latent Overall Toxicity (LOTox) profiles in osteosarcoma: a new taxonomy based on latent Markov models | Abstract | | Due to the presence of multiple types of adverse events with different levels of severity, the analysis of longitudinal toxicity data is a difficult task in cancer studies. In this work, a novel approach based on latent Markov models and compositional data techniques is proposed. The latent status of interest is the Latent Overall Toxicity (LOTox) condition of each patient. The main objectives are to identify different latent states of overall toxicity burden and to investigate the evolution of individual toxicity risk during cancer treatment. This methodology is applied to osteosarcoma treatment data to provide novel techniques that may support medical decisions in childhood cancer therapy. |
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75/2022 - 10/19/2022
Rea, F.; Savaré, L; Franchi, M.; Corrao, G; Mancia, G
Adherence to Treatment by Initial Antihypertensive Mono and Combination Therapies | Abstract | | BACKGROUND
Aim of our study was to compare adherence to antihypertensive drug
therapy between newly treated patients in whom monotherapy or a
2-drug single-pill combination (SPC) was initially dispensed.
METHODS
The 63,448 residents of Lombardy Region (Italy), aged 40–80 years,
who were newly treated with antihypertensive drugs during 2016,
were identified and followed for 1 year after the first prescription. The
outcome of interest was adherence to drug therapy that was measured
according to the “proportion of days covered” (PDC) criterion, i.e.,
the ratio between the number of days in which the drug was available
and the days of follow-up. Patients who had a PDC >75% and
<25% were defined as highly and poorly adherent to drug therapy,
respectively. Log-binomial regression models were fitted to compare
the propensity to treatment adherence between the initial therapeutic
strategies, after adjusting for baseline demographic and clinical
covariates.
RESULTS
About 46% and 17% of patients showed high and poor adherence, respectively.
Compared with patients under initial monotherapy (85%),
those who were initially treated with a SPC (15%) had higher propensity
to be highly adherent and a lower propensity to be poorly adherent
to antihypertensive treatment (risk ratio: 1.18, 95% confidence interval
1.16–1.21; 0.42, 0.39–0.45, respectively). This was the case regardless the
sex, the age, the patient clinical status, and with almost any type of SPC.
CONCLUSIONS
In a real-life setting, patients who were initially prescribed a 2-drug
SPC exhibited more frequently a good adherence to antihypertensive
treatment than those starting with a single drug.
NOTE: This work has been partially carried out while one of the authors (L. Savarè) was affiliated with MOX Laboratory |
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74/2022 - 10/19/2022
Salvador, M.; Regazzoni, F.; Dede', L.; Quarteroni, A.
Fast and robust parameter estimation with uncertainty quantification for the cardiac function | Abstract | | Parameter estimation and uncertainty quantification are crucial in computational cardiology, as they enable the construction of digital twins that faithfully replicate the behavior of physical patients. Robust and efficient mathematical methods must be designed to fit many model parameters starting from a few, possibly non-invasive, noisy observations. Moreover, the effective clinical translation requires short execution times and a small amount of computational resources. In the framework of Bayesian statistics, we combine Maximum a Posteriori estimation and Hamiltonian Monte Carlo to find an approximation of model parameters and their posterior distributions. To reduce the computational effort, we employ an accurate Artificial Neural Network surrogate of 3D cardiac electromechanics model coupled with a 0D cardiocirculatory model. Fast simulations and minimal memory requirements are achieved by using matrix-free methods, automatic differentiation and automatic vectorization. Furthermore, we account for the surrogate modeling error and measurement error. We perform three different in silico test cases, ranging from the ventricular function to the entire cardiovascular system, involving whole-heart mechanics, arterial and venous circulation. The proposed method is robust when high levels of signal-to-noise ratio are present in the quantities of interest in combination with a random initialization of the model parameters in suitable intervals. As a matter of fact, by employing a single central processing unit on a standard laptop and a few hours of computations, we attain small relative errors for all model parameters and we estimate posterior distributions that contain the true values inside the 90% credibility regions. With these benefits, our approach meets the requirements for clinical exploitation, while being compliant with Green Computing practices. |
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