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 1249 prodotti
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72/2024 - 26/09/2024
Patanè, G.; Bortolotti, T.; Yordanov, V.; Biagi, L. G. A.; Brovelli, M. A.; Truong, A. Q; Vantini, S.
An interpretable and transferable model for shallow landslides detachment combining spatial Poisson point processes and generalized additive models | Abstract | | Less than 10 meters deep, shallow landslides are rapidly moving and strongly dangerous slides. In the present work, the probabilistic distribution of the landslide detachment points within a valley is modelled as a spatial Poisson point process, whose intensity depends on geophysical predictors according to a generalized additive model. Modelling the intensity with a generalized additive model jointly allows to obtain good predictive performance and to preserve the interpretability of the effects of the geophysical predictors on the intensity of the process. We propose a novel workflow, based on Random Forests, to select the geophysical predictors entering the model for the intensity. In this context, the statistically significant effects are interpreted as activating or stabilizing factors for landslide detachment. In order to guarantee the transferability of the resulting model, training, validation, and test of the algorithm are performed on mutually disjoint valleys in the Alps of Lombardy (Italy). Finally, the uncertainty around the estimated intensity of the process is quantified
via semiparametric bootstrap. |
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71/2024 - 19/09/2024
Zhang, L.; Pagani, S.; Zhang, J.; Regazzoni, F.
Shape-informed surrogate models based on signed distance function domain encoding | Abstract | | We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the computational domain. Our approach is based on the combination of two neural networks (NNs). The first NN, conditioned on a latent code, provides an implicit representation of geometry variability through signed distance functions. This automated shape encoding technique generates compact, low-dimensional representations of geometries within a latent space, without requiring the explicit construction of an encoder. The second NN reconstructs the output physical fields independently for each spatial point, thus avoiding the computational burden typically associated with high-dimensional discretizations like computational meshes. Furthermore, we show that accuracy in geometrical characterization can be further enhanced by employing Fourier feature mapping as input feature of the NN. The meshless nature of the proposed method, combined with the dimensionality reduction achieved through automatic feature extraction in latent space, makes it highly flexible and computationally efficient. This strategy eliminates the need for manual intervention in extracting geometric parameters, and can even be applied in cases where geometries undergo changes in their topology. Numerical tests in the field of fluid dynamics and solid mechanics demonstrate the effectiveness of the proposed method in accurately predict the solution of PDEs in domains of arbitrary shape. Remarkably, the results show that it achieves accuracy comparable to the best-case scenarios where an explicit parametrization of the computational domain is available. |
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68/2024 - 16/09/2024
Gambarini, M.; Ciaramella, G.; Miglio, E.
A gradient flow approach for combined layout-control design of wave energy parks | Abstract | | Wave energy converters (WECs) represent an innovative technology for power generation from renewable sources (marine energy). Although there has been a great deal of research into such devices in recent decades, the power output of a single device has remained low. Therefore, installation in parks is required for economic reasons. The optimal design problem for parks of WECs is challenging since it requires the simultaneous optimization of positions and control parameters. While the literature on this problem usually considers metaheuristic algorithms, we present a novel numerical framework based on a gradient-flow formulation. This framework is capable of solving the optimal design problem for WEC parks. In particular, we use a low-order adaptive Runge-Kutta scheme to integrate the gradient-flow equation and introduce an inexact solution procedure. Here, the tolerances of the linear solver used for projection on the constraint nullspace and of the time-advancing scheme are automatically adapted to avoid over-solving so that the method requires minimal tuning. We then provide the specific details of its application to the considered WEC problem: the goal is to maximize the average power produced by a park, subject to hydrodynamic and dynamic governing equations and to the constraints of available sea area, minimum distance between devices, and limited oscillation amplitude around the undisturbed free surface elevation. A suitable choice of the discrete models allows us to compute analytically the Jacobian of the state problem's residual. Numerical tests with realistic parameters show that the proposed algorithm is efficient, and results of physical interest are obtained.
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69/2024 - 16/09/2024
Galliani, G.; Secchi, P.; Ieva, F.
Estimation of dynamic Origin–Destination matrices in a railway transportation network integrating ticket sales and passenger count data | Abstract | | Accurately estimating Origin–Destination matrices is a pressing challenge in transportation management and urban planning. However, traditional methods like travel surveys have limitations in availability and comprehensiveness, which have been further exacerbated by the recent changes in mobility patterns induced by the COVID-19 pandemic.
To address this issue, we focused on the Trenord railway network in Lombardy, Italy, and developed an innovative pipeline to integrate ticket and subscription sales and Automated Passenger Counting data using the Iterative Proportional Fitting algorithm. By effectively navigating the complexities of diverse and incomplete data sources, our approach showcases adaptability across various transportation contexts. Our research offers a valuable tool for operators, policymakers, and
researchers, bridging the gap between data availability and the need for precise OD matrices.
Additionally, we emphasise the potential of dynamic OD matrices and showcase methods for detecting anomalies in mobility trends, interpreting them in the context of events from the last months of 2022. |
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70/2024 - 16/09/2024
Panzeri, L.; Fumagalli, A.; Longoni, L.; Papini, M.; Diego, A.
Sensitivity analysis with a 3D mixed-dimensional code for DC geoelectrical investigations of landfills: synthetic tests | Abstract | | Electrical resistivity tomography is a suitable technique for non-invasive monitoring of municipal solid waste landfills, but accurate sensitivity analysis is necessary to evaluate the effectiveness and reliability of geoelectrical investigations and to properly design data acquisition. Commonly, a thin high-resistivity membrane in placed underneath the waste to prevent leachate leakage. In the construction of a numerical framework for sensitivity computation, taking into account the actual dimensions of the electrodes and, in particular, of the membrane, can lead to extremely high computational costs. In this work, we present a novel approach for numerically computing sensitivity effectively by adopting a mixed-dimensional framework, where the membrane is approximated as a 2D object and the electrodes as 1D objects. The code is first validated against analytical expressions for simple 4-electrode arrays and a homogeneous medium. It is then tested in simplified landfill models, where a 2D box-shaped liner separates the landfill body from the surrounding media, and 48 electrodes are used. The results show that electrodes arranged linearly along both sides of the perimeter edges of the box-shaped liner are promising for detecting liner damage, with sensitivity increasing by 2-3 orders of magnitude, even for damage as small as one-sixth of the electrode spacing in diameter. Good results are also obtained when simulating an electrical connection between the landfill and the surrounding media that is not due to liner damage. The next steps involve evaluating the minimum number of configurations needed to achieve suitable sensitivity with a manageable field effort and validating the modeling results with downscaled laboratory tests. |
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64/2024 - 13/09/2024
Cavazzutti, M.; Arnone, E.; Ferraccioli, F.; Galimberti, C.; Finos, L.; Sangalli, L.M.
Sign-Flip inference for spatial regression with differential regularization | Abstract | | We address the problem of performing inference on the linear and nonlinear terms of a semiparametric
spatial regression model with differential regularization. For the linear term, we propose a new resampling procedure, based on (partial) sign-flipping of an appropriate transformation of the residuals of the model. The proposed resampling scheme can mitigate the bias effect, induced by the differential regularization. We prove that the proposed test is asymptotically exact. Moreover, we show by simulation studies that it enjoys very good control of Type-I error also in small sample scenarios, differently from parametric alternatives. Furthermore, we show that the proposed test has higher power with respect to recently proposed nonparametric tests on the linear term of semiparametric regression models with differential regularization. Concerning the nonlinear term, we develop three different inference approaches: a parametric test, and two nonparametric alternatives. The nonparametric tests are based on a sign-flip approach. One of these tests is proved to be asymptotically exact, while the other is proved to be exact also for finite samples. Simulation
studies highlight the very good control of Type-I error of the nonparametric approaches, while retaining high power. |
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65/2024 - 13/09/2024
Possenti, L.; Vitullo, P.; Cicchetti, A.; Zunino, P.; Rancati, T.
Modeling Hypoxia Induced Radiation Resistance and the Impact of Radiation Sources | Abstract | | Hypoxia contributes significantly to resistance in radiotherapy. Our research rigorously examines the influence of microvascular morphology on radiotherapy outcome, specifically focusing on how microvasculature shapes hypoxia within the microenvironment and affects resistance to a standard treatment regimen (30 X 2 Gy).
Our computational modeling extends to the effects of different radiation sources. For photons and protons, our analysis establishes a clear correlation between hypoxic volume distribution and treatment effectiveness, with vascular density and regularity playing a crucial role in treatment success.
On the contrary, carbon ions exhibit distinct effectiveness, even in areas of intense hypoxia and poor vascularization. This finding points to the potential of carbon-based hadron therapy in overcoming hypoxia-induced resistance to RT.
Considering that the spatial scale analyzed in this study is closely aligned with that of imaging data voxels, we also address the implications of these findings in a clinical context envisioning the possibility of detecting subvoxel hypoxia. |
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63/2024 - 12/09/2024
Vitullo, P.; Franco, N.R.; Zunino, P.
Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy | Abstract | | Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work is to mitigate the computational cost of UQ for a 3D-1D multiscale computational model of microcirculation. To this purpose, we present a deep learning enhanced multi-fidelity Monte Carlo (DL-MFMC) method that integrates the information of a multiscale full-order model (FOM) with that coming from a deep learning enhanced non-intrusive projection-based reduced order model (ROM). The latter is constructed by leveraging on proper orthogonal decomposition (POD) and mesh-informed neural networks (previously developed by the authors and co-workers), integrating diverse architectures that approximate POD coefficients while introducing fine-scale corrections for the microstructures. The DL-MFMC approach provides a robust estimator of specific quantities of interest and their associated uncertainties, with optimal management of computational resources. In particular, the computational budget is efficiently divided between training and sampling, ensuring a reliable estimation process suitably exploiting the ROM speed-up. Here, we apply the DL-MFMC technique to accelerate the estimation of biophysical quantities regarding oxygen transfer and radiotherapy outcomes. Compared to classical Monte Carlo methods, the proposed approach shows remarkable speed-ups and a substantial reduction of the overall computational cost. |
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