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 1249 products
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51/2022 - 07/28/2022
Losapio, D.; Scotti, A.
Local Embedded Discrete Fracture Model (LEDFM) | Abstract | | The study of flow in fractured porous media is a key ingredient for many geoscience applications, such as reservoir management and geothermal energy production. Modelling and simulation of these highly heterogeneous and geometrically complex systems require the adoption of non-standard numerical schemes. The Embedded Discrete Fracture Model (EDFM) is a simple and effective way to account for fractures with coarse and regular grids, but it suffers from some limitations: it assumes a linear pressure distribution around fractures, which holds true only far from the tips and fracture intersections, and it can be employed for highly permeable fractures only. In this paper we propose an improvement of EDFM which aims at overcoming these limitations computing an improved coupling between fractures and the surrounding porous medium by a) relaxing the linear pressure
distribution assumption, b) accounting for impermeable fractures modifying near-fracture transmissibilities. These results are achieved by solving different types of local problems with a fine conforming grid, and computing new transmissibilities (for connections between fractures and the surrounding porous medium and those through the porous medium itself near to the fractures). Such local problems are inspired from numerical upscaling techniques present in the literature. The new method is called Local Embedded Discrete Fracture Model (LEDFM) and the results obtained from several numerical tests confirm the aforementioned improvements. |
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50/2022 - 07/28/2022
Elías, A.; Jiménez, R.; Paganoni, A.M.; Sangalli, L.M.
Integrated Depths for Partially Observed Functional Data | Abstract | | Partially observed functional data are frequently encountered in applications and are the object of an increasing interest by the literature. We here address the problem of measuring the centrality of a datum in a partially observed functional sample. We propose an integrated functional depth for partially observed functional data, dealing with the very challenging case where partial observability can occur systematically on any observation of the functional dataset. In particular, differently f rom m any techniques f or partially observed functional data, we do not request that some functional datum is fully observed, nor we require that a common domain exist, where all of the functional data are recorded. Because of this, our proposal can also be used in those frequent situations where reconstructions methods and other techniques for partially observed functional data are inapplicable. By means of simulation studies, we demonstrate the very good performances the proposed depth on finite samples. Our proposal enables the use of benchmark methods based on depths, originally introduced for fully observed data, in the case of partially observed functional data. This include the functional boxplot, the outliergram and the depth vs depth classifiers. We illustrate our proposal on two case studies, the first concerning a problem of outlier detection in German electricity supply functions, the second regarding a classification problem with data obtained from medical imaging. |
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49/2022 - 07/18/2022
Botti, M.; Fumagalli, A.; Scotti, A.
Uncertainty quantification for mineral precipitation and dissolution in fractured porous media | Abstract | | In this work, we present an uncertainty quantification analysis to determine the influence and importance of some physical parameters in a reactive transport model in fractured porous media. An accurate description of flow and transport in the fractures is key to obtain reliable simulations, however,
fractures geometry and physical characteristics pose several challenges from both the modeling and implementation side. We adopt a mixed-dimensional approximation, where fractures and their intersections are represented as objects of lower dimension. To simplify the presentation, we consider only two
chemical species: one solute, transported by water, and one precipitate attached to the solid skeleton. A global sensitivity analysis to uncertain input data is performed exploiting the Polynomial Chaos expansion along with spectral projection methods on sparse grids. |
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48/2022 - 07/18/2022
Gregorio, C.; Barbati, G.; Ieva, F.
A wavelet-mixed landmark survival model for the effect of short-term oscillations in longitudinal biomarker’s profiles | Abstract | | Statistical methods to study the association between a longitudinal biomarker and the risk of death are very relevant for the long-term monitoring of frail subjects. In this context, sudden crises can cause the biomarker to undergo very abrupt changes. Although these oscillations are typically short-term, they often contain relevant prognostic information for the survival endpoint of interest. We propose a method that couples a linear mixed-model with a wavelet smoothing to extract both the long-term component and the short-term oscillations from the individual longitudinal biomarker profiles. We then use them as predictors in a landmark survival model to study their dynamic association with the risk of death. To illustrate the method, we use the clinical application which motivated our work, i.e., the monitoring of potassium in Heart Failure patients. The dataset consists of real-world data coming from the integration of Administrative Health Records with Outpatient and Inpatient Clinic E-chart. Our method not only allows us to identify the short-term oscillations but also reveals their prognostic role in predicting the risk of death, according to their duration and, demonstrating the importance of including such short-term oscillations into the modeling. Compared to standard landmark analyses and joint models, the proposed method achieves higher predictive performances. In the context of the potassium monitoring, our analysis has important clinical implications since it allows us to derive a dynamic score that can be used in clinical practice to assess the risk related to an observed patient's potassium trajectory. |
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47/2022 - 07/18/2022
Botti, M.; Di Pietro, D.A.; Salah, M.
A serendipity fully discrete div-div complex on polygonal meshes | Abstract | | In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincar'e--Korn-type inequalities for hybrid fields. |
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46/2022 - 07/13/2022
Lucca, A.; Fraccarollo, L.; Fossan, F.E.; Braten, A.T.; Pozzi, S.; Vergara, C.; Muller, L.O.
Impact of pressure guidewire on model-based FFR prediction | Abstract | | Fractional Flow Reserve (FFR) is used to characterize the functional significance of coronary artery stenoses. FFR is assessed under hyperemic conditions by invasive measurements of trans-stenotic pressure thanks to the insertion of a pressure guidewire across the coronary stenosis during catheterization. In order to overcome the potential risk related to the invasive procedure and to reduce the associated high costs, blood flow simulations that incorporate clinical imaging and patient-specific characteristics have been proposed. Most CCTA-derived FFR models neglect the potential influence of the guidewire on the flow and pressure. We aim to quantify the impact of taking into account the presence of the guidewire in model-based FFR prediction. We adopt a CCTA-derived FFR model and perform simulations with and without the guidewire for 18 patients with suspected stable CAD. Presented results show that the presence of the guidewire leads to a tendency to predict a lower FFR value. The FFR reduction is prominent in cases of severe stenoses, while the influence of the guidewire is less pronounced in cases of moderate stenoses. Particular attention should be drawn to intermediate stenoses, in which the presence of the guidewire can change the diagnostic outcome and consequently the clinical decision. |
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45/2022 - 07/13/2022
Franco, N.; Fresca, S.; Manzoni, A.; Zunino, P.
Approximation bounds for convolutional neural networks in operator learning | Abstract | | Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature still lack a rigorous justification on their mathematical foundations. Motivated by this fact, in this paper we derive rigorous error bounds for the approximation of nonlinear operators by means of CNN models. More precisely, we address the case in which an operator maps a finite dimensional input onto a functional output, and a neural network model is used to approximate a discretized version of the input-to-output map. The resulting error estimates provide a clear interpretation of the hyperparameters defining the neural network architecture. All the proofs are constructive, and they ultimately reveal a deep connection between CNNs and the discrete Fourier transform. Finally, we complement the derived error bounds by numerical experiments that illustrate their application. |
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44/2022 - 06/26/2022
Peli, R.; Dovera, L.; Fighera, G.; Menafoglio, A.; Secchi, P.
Forecasting Oil Production Rates in Primary Depletion using the Physics-based Residual Kriging functional approach | Abstract | | In this work, we illustrate a novel functional data analysis approach for the forecast of oil production rates in a mature single-phase reservoir. This model is based on the recently developed Physics-based Residual Kriging predictor, which represents oil rates as functional data and decomposes them as the sum of the predictions of a physical model and the geostatistical modelization of its residuals. In this context, we use the recently introduced FlowNet model to build up the physical term which, through a network-based representation of the reservoir, avoids the burden of three-dimensional full-physics simulations.
Furthermore, we propose an extension of the Physics-based Residual Kriging predictor in presence of ensemble of physical models, i.e. when the uncertainty in the model parameters is accounted for by simulating several models corresponding to different parameters samples.
The Physics-based Residual Kriging predictor is here applied to the oil rates produced in a realistic reservoir. We analyze three different scenarios in terms of wells drilling schedule, from a simple to a realistic scheme. In each scenario, we compare the predictions given by Physics-based Residual Kriging to the ones obtained with FlowNet and a pure geostatistical approach. |
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