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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82/2024 - 08/11/2024
Rosafalco, L.; Conti, P.; Manzoni, A.; Mariani, S.; Frangi, A.
EKF-SINDy: Empowering the extended Kalman filter with sparse identification of nonlinear dynamics | Abstract | | Measured data from a dynamical system can be assimilated into a predictive model by means of Kalman filters. Nonlinear extensions of the Kalman filter, such as the Extended Kalman Filter (EKF), are required to enable the joint estimation of (possibly nonlinear) system dynamics and of input parameters. To construct the evolution model used in the prediction phase of the EKF, we propose to rely on the Sparse Identification of Nonlinear Dynamics (SINDy). SINDy enables to identify the evolution model directly from preliminary acquired data, thus avoiding possible bias due to wrong assumptions and incorrect modelling of the system dynamics. Moreover, the numerical integration of a SINDy model leads to great computational savings compared to alternate strategies based on, e.g., finite elements. Last, SINDy allows an immediate definition of the Jacobian matrices required by the EKF to identify system dynamics and properties, a derivation that is usually extremely involved with physical models. As a result, combining the EKF with SINDy provides a data-driven computationally efficient, easy-to-apply approach for the identification of nonlinear systems, capable of robust operation even outside the range of training of SINDy. To demonstrate the potential of the approach, we address the identification of a linear non-autonomous system consisting of a shear building model excited by real seismograms, and the identification of a partially observed nonlinear system. The challenge arising from the use of SINDy when the system state is not entirely accessible has been relieved by means of time-delay embedding. The great accuracy and the small uncertainty associated with the state identification, where the state has been augmented to include system properties, underscores the great potential of the proposed strategy, paving the way for the setting of predictive digital twins in different fields. |
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80/2024 - 04/11/2024
Crippa, B.; Scotti, A.; Villa, A
Numerical Solution of linear drift-diffusion and pure drift equations on one-dimensional graphs | Abstract | | We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite Volume schemes with upwind flux to domains presenting bifurcation nodes with an arbitrary number of incoming and outgoing edges, and implicit time discretization. We show that the discrete problems admit positive unique solutions, and we test the methods on the intricate geometry of an electrical treeing. |
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79/2024 - 28/10/2024
Baioni, P.J.; Benacchio, T.; Capone, L.; de Falco, C.
Portable, Massively Parallel Implementation of a Material Point Method for Compressible Flows | Abstract | | The recent evolution of software and hardware technologies is leading to a renewed computational interest in Particle-In-Cell (PIC) methods such as the Material Point Method (MPM). Indeed, pro- vided some critical aspects are properly handled, PIC methods can be cast in formulations suitable for the requirements of data locality and fine-grained parallelism of modern hardware accelerators such as Graphics Processing Units (GPUs). Such a rapid and continuous technological development increases also the importance of generic and portable implementations. While the capabilities of MPM on a wide range continuum mechanics problem have been already well as- sessed, the use of the method in compressible fluid dynamics has re- ceived less attention. In this paper we present a portable, highly par- allel, GPU based MPM solver for compressible gas dynamics. The implementation aims to reach a good compromise between porta- bility and efficiency in order to provide a first assessment of the potential of this approach in solving strongly compressible gas flow problems, also taking into account solid obstacles. The numerical model considered constitutes a first step towards the development of a monolithic MPM solver for Fluid-Structure Interaction (FSI) problems at all Mach numbers up to the supersonic regime. |
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78/2024 - 16/10/2024
Ziarelli, G.; Pagani, S.; Parolini, N.; Regazzoni, F.; Verani, M.
A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts | Abstract | | Recent advancements in scientific machine learning offer a promising framework to integrate data within epidemiological models, offering new opportunities for the implementation of tailored preventive measures and the mitigation of the risks associated with epidemic outbreaks. Among the many parameters to be calibrated and extrapolated in an epidemiological model, a special role is played by the transmission rate, whose inaccurate extrapolation can significantly impair the quality of the resulting forecasts. In this work, we aim to formalize a novel scientific machine learning framework to reconstruct the hidden dynamics of the transmission rate, by incorporating the influence of exogenous variables (such as environmental conditions and strain-specific characteristics). We propose an hybrid model that blends a data-driven layer with a physics-based one. The data-driven layer is based on a neural ordinary differential equation that learns the dynamics of the transmission rate, conditioned on the meteorological data and wave-specific latent parameters. The physics-based layer, instead, consists of a standard SEIR compartmental model, wherein the transmission rate represents an input. The learning strategy follows an end-to-end approach: the loss function quantifies the mismatch between the actual numbers of infections and its numerical prediction obtained from the SEIR model incorporating as an input the transmission rate predicted by the neural ordinary differential equation. We validate this novel approach using both a synthetic test case and a realistic test case based on meteorological data (temperature and humidity) and influenza data from Italy between 2010 and 2020. In both scenarios, we achieve low generalization error on the test set and observe strong alignment between the reconstructed model and established findings on the influence of meteorological factors on epidemic spread. Finally, we implement a data assimilation strategy to adapt the neural equation to the specific characteristics of an epidemic wave under investigation, and we conduct sensitivity tests on the network’s hyperparameters. |
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77/2024 - 16/10/2024
Piersanti, R.; Bradley, R.; Ali, S.Y.; Quarteroni A.; Dede', L; Trayanova, N.A.
Defining myocardial fiber bundle architecture in atrial digital twins | Abstract | | A key component in developing atrial digital twins (ADT) - virtual representations of patients’ atria - is the accurate prescription of myocardial fibers which are essential for the tissue characterization. Due to the difficulty of reconstructing atrial fibers from medical imaging, a widely used strategy for fiber generation in ADT relies on mathematical models. Existing methodologies utilze semi-automatic approaches, are tailored to specific morphologies, and lack rigorous validation against imaging fiber data. In this study, we introduce a novel atrial Laplace-Dirichlet-Rule-Based Method (LDRBM) for prescribing highly detailed myofiber orientations and providing robust regional annotation in bi-atrial morphologies of any complexity. The robustness of our approach is verified in eight extremely detailed bi-atrial geometries, derived from a sub-millimiter Diffusion-Tensor-Magnetic-Resonance Imaging (DTMRI) human atrial fiber dataset. We validate the LDRBM by quantitatively recreating each of the DTMRI fiber architectures: a comprehensive comparison with DTMRI ground truth data is conducted, investigating differences between electrophysiology (EP) simulations provided by either LDRBM and DTMRI fibers. Finally, we demonstrate that the novel LDRBM outperforms current state-of-the-art fiber models, confirming the exceptional accuracy of our methodology and the critical importance of incorporating detailed fiber orientations in EP simulations. Ultimately, this work represents a fundamental step toward the development of physics-based digital twins of the human atria, establishing a new standard for prescribing fibers in ADT. |
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75/2024 - 14/10/2024
Cattarossi, L.; Sacco, F.; Giuliani, N.; Parolini, N.; Mola, A.
A geometry aware arbitrary order collocation Boundary Element Method solver for the potential flow past three dimensional lifting surfaces | Abstract | | This work presents a numerical model for the simulation of potential flow past three dimensional lifting surfaces. The solver is based on the collocation Boundary Element Method, combined with Galerkin variational formulation of the nonlinear Kutta condition imposed at the trailing edge. A similar Galerkin variational formulation is also used for the computation of the fluid velocity at the wake collocation points, required by the relaxation algorithm which aligns the wake with the local flow. The use of such a technique, typically associated with the Finite Element Method, allows in fact for the evaluation of the solution derivatives in a way that is independent of the local grid topology. As a result of this choice, combined with the direct interface with CAD surfaces, the solver is able to use arbitrary order Lagrangian elements on automatically refined grids. Numerical results on a rectangular wing with NACA 0012 airfoil sections are presented to compare the accuracy improvements obtained by grid spatial refinement or by discretization degree increase. Finally, numerical results on rectangular and swept wings with NACA 0012 airfoil section confirm that the model is able to reproduce experimental data with good accuracy. |
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74/2024 - 08/10/2024
Crippa, B., Scotti, A.; Villa, A
A mixed-dimensional model for the electrostatic problem on coupled domains | Abstract | | We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of thin inclusions in a larger 3D domain. The numerical solution is obtained by Mixed Finite Elements for the 3D problem and Finite Elements on the 1D domain. We analyze some test cases with simple geometries to validate the proposed approach against analytical solutions, and perform comparisons with the fully resolved 3D problem. We treat the case where ramifications are present in the one-dimensional domain and show some results on the geometry of an electrical treeing, a ramified structure that propagates in insulators causing their failure. |
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73/2024 - 07/10/2024
Liverotti, L.; Ferro, N.; Soli, L.; Matteucci, M.; Perotto, S.
Using SAR Data as an Effective Surrogate for Optical Data in Nitrogen Variable Rate Applications: a Winter Wheat Case Study | Abstract | | This study highlights the feasibility of using SAR data as a surrogate for optical acquisitions in the generation of nitrogen prescription maps in wheat cultivation. Unlike the optical-based approaches which are negatively affected by adverse meteorological conditions, the proposed strategy provides the possibility to compute the fertilization maps at any date, by exploiting the all-weather, day-and-night SAR capabilities. We train a U-Net-like CNN architecture on Sentinel-2 optical and Sentinel-1 SAR datasets, after a properly alignment in time. The trained model returns a surrogate NDVI distribution starting from SAR acquisitions, when optical data are not available. The recovered NDVI information is converted into LAI and GAI distributions, by resorting to an exponential and a linear law, respectively, according to the literature. Finally, the nitrogen prescription map is obtained out of the recovered GAI values. A qualitative and quantitative analysis of the error between the optical and SAR-derived prescription maps shows that the procedure is accurate, especially during the tillering and the stem elongation growth phases. |
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