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 1268 products
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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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43/2022 - 06/20/2022
Zappon E.; Manzoni A.; Gervasio P.; Quarteroni A.
A reduced order model for domain decompositions with non-conforming interfaces | Abstract | | In this paper we propose a reduced order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems with Dirichlet and Neumann interface conditions, respectively. After discretization by (e.g.) the finite element method, the full-order model (FOM) is solved by Dirichlet-
Neumann iterations between the two sub-problems until interface convergence is reached. We, then, apply the reduced basis (RB) method to obtain a low-dimensional representation of the solution of each sub-problem. Furthermore, we use the discrete empirical interpolation method (DEIM) applied at the interface level to achieve a fully reduced-order representation of the DD techniques implemented. To deal with interface data when non-conforming FE interface discretizations are considered, we employ the INTERNODES method combined with the interface DEIM reduction. The reduced-order model (ROM) is then solved by sub-iterating between the two reduced-order sub-problems until convergence of the approximated high-fidelity interface solutions. The ROM scheme is numerically verified on both steady and unsteady coupled problems, in the case of non-conforming FE interfaces. |
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42/2022 - 06/14/2022
Gatti, F.; Fois, M.; de Falco, C.; Perotto, S.; Formaggia, L.
Parallel simulations for fast-moving landslides: space-time mesh adaptation and sharp tracking of the wetting front | Abstract | | We propose a highly scalable solver for a two-dimensional depth-integrated fluid dynamic model in order to simulate flow-like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two-step second-order Taylor-Galerkin scheme, enriched by a suitable flux correction in order to avoid spurious oscillations, in particular near discontinuities and close to the wetting-drying interface.
A mesh adaptation procedure based on a gradient-recovery a posteriori error estimator allows us to efficiently deal with a discretization of the domain customized to the phenomenon under investigation. Moreover, we resort to an adaptive scheme also in time to prevent filtering out the landslide dynamics, and to
an interface tracking algorithm
to avoid an excessive refinement in non-interfacial regions while preserving details along the wetting-drying front. Finally, after verifying the performance of the proposed numerical framework on idealized settings, we carry out a scalability analysis of the code both on idealized and real scenarios, to check the efficiency of the overall implementation. |
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41/2022 - 06/14/2022
Arnone, A.; Ferraccioli, F.; Pigolotti, C.; Sangalli, L.M.
A roughness penalty approach to estimate densities over two-dimensional manifolds | Abstract | | An innovative nonparametric method for density estimation over general two-dimensional Riemannian manifolds is proposed. The method follows a functional data analysis approach, combining maximum likelihood estimation with a roughness penalty that involves a differential operator appropriately defined over the manifold domain, thus controlling the smoothness of the estimate. The proposed method can accurately handle point pattern data over complicated curved domains. Moreover, it is able to capture complex multimodal signals, with strongly localized and highly skewed modes, with varying directions and intensity of anisotropy. The estimation procedure exploits a discretization in finite element bases, enabling great flexibility on the spatial domain. The method is tested through simulation studies, showing the strengths of the proposed approach. Finally, the density estimation method is illustrated with an application to the distribution of earthquakes in the world. |
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40/2022 - 06/14/2022
Fumagalli, A.; Patacchini, F. S.
Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media | Abstract | | Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure gradient and velocity. The actual shape of this relation is normally chosen at the outset of the problem, even though, in practice, the fluid may experience velocities outside of its range of applicability. We propose here an adaptive model, so that the most appropriate law is locally selected depending on the computed velocity. From the analytical point of view, we show well-posedness of the problem when the law is monotone in velocity and show existence in one space dimension otherwise. From the computational point of view, we present a new approach based on regularizing via mollification the underlying dissipation, i.e., the power lost by the fluid to the porous medium through drag. The resulting regularization is shown to converge to the original problem using $Gamma$-convergence on the dissipation in the monotone case. This approach gives rise to a variational numerical scheme which applies to very general problems and which we validate on three test cases. |
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39/2022 - 06/02/2022
Ferro, N.; Perotto, S.; Gavazzoni, M.
A new fluid-based strategy for the connection of non-matching lattice materials | Abstract | | We present a new algorithm for the design of the connection region between different lattice materials. We solve a Stokes-type topology optimization problem on a narrow morphing region to smoothly connect two different unit cells. The proposed procedure turns out to be effective and provides a local re-design of the materials, leading to a very mild modification of the mechanical behaviour characterizing the original lattices. The robustness of the algorithm is assessed in terms of sensitivity of the final layout to different parameters. Both the cases of Cartesian and non-Cartesian morphing regions are successfully investigated. |
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