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 1268 prodotti
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105/2024 - 15/12/2024
Bartsch, J.; Barakat, A.A.; Buchwald, S.; Ciaramella, G.; Volkwein, S.; Weig, E.M.
Reconstructing the system coefficients for coupled harmonic oscillators | Abstract | | Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this research question within the framework of inverse problems. In this work, we consider optimization techniques to solve the inverse problem using Tikhonov regularization and data from laboratory experiments. We propose an iterative strategy that eliminates the need for laboratory experiments. Our method is applied to identify the coupling and damping coefficients in a system of oscillators, ensuring an efficient and experiment-free approach. We present our results and compare them with those obtained from an alternative, purely experimental approach. By employing our proposed strategy, we demonstrate a significant reduction in the number of laboratory experiments required. |
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104/2024 - 07/12/2024
Cerrone, D.; Riccobelli, D.; Vitullo, P.; Ballarin, F.; Falco, J.; Acerbi, F.; Manzoni, A.; Zunino, P.; Ciarletta, P.
Patient-specific prediction of glioblastoma growth via reduced order modeling and neural networks | Abstract | | Glioblastoma (GBL) is one of the deadliest brain cancers in adults. The GBL cells invade the physical structures within the brain extracellular environment with patient-specific features. In this work, we propose a proof-of-concept for mathematical framework of precision oncology enabling rapid parameter estimation from neuroimaging data in clinical settings.
The proposed diffuse interface model of GBL growth is informed by neuroimaging data, periodically collected in a clinical study from diagnosis to surgery and adjuvant treatment. We build a robust and efficient computational pipeline to aid clinical decision-making based on integrating model reduction techniques and neural networks. Patient specificity is captured through the segmentation of the magnetic resonance imaging into a computational replica of the patient brain, mimicking the brain microstructure by incorporating also the diffusion tensor imaging data.
The full order model (FOM) is first discretized using the finite element method and later approximated by a reduced order model (ROM) adopting proper orthogonal decomposition (POD). Trained by clinical data, we finally use neural networks to map the parameter space of GBL evolution over time and to predict the patient-specific model parameters from the observed clinical evolution of the tumor mass. |
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103/2024 - 03/12/2024
Fois, M.; Gatti, F.; de Falco, C.; Formaggia, L.
A comparative analysis of mesh-based and particle-based numerical methods for landslide run-out simulations | Abstract | | Landslides are among the most dangerous natural disasters, with their unpredictability and potential for catastrophic human and economic losses exacerbated by climate change. Continuous monitoring and precise modeling of landslide-prone areas are crucial for effective risk management and mitigation. This study explores two distinct numerical simulation approaches: the mesh-based finite element model and the particle-based model. Both methods are analyzed for their ability to simulate landslide dynamics, focusing on their respective advantages in handling complex terrain, material interactions, and large deformations. A modified version of the second-order Taylor-Galerkin scheme and the depth-averaged Material Point Method are employed to model gravity-driven free surface flows, based on depth-integrated incompressible Navier-Stokes equations. The methods are rigorously tested against benchmarks and applied to a real-world scenario to assess their performance, strengths, and limitations. The results offer insights into selecting appropriate simulation techniques for landslide analysis, depending on specific modeling requirements and computational resources. |
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101/2024 - 29/11/2024
Bonetti, S.; Corti, M.
Unified discontinuous Galerkin analysis of a thermo/poro-viscoelasticity model | Abstract | | We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model, and we develop a stability analysis in the continuous setting that holds both for the full inertial and quasi-static problems and that is robust with respect to most of the physical parameters of the problem. For spatial discretization, we propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. For the semi-discrete problem, we prove the extension of the stability result demonstrated in the continuous setting. A wide set of numerical simulations is presented to assess the convergence and robustness properties of the proposed method. Moreover, we test the scheme with literature and physically sound test cases for proof-of-concept applications in the geophysical context. |
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102/2024 - 29/11/2024
Bucelli, M.
The lifex library version 2.0 | Abstract | | This article presents updates to lifex [Africa, SoftwareX (2022)], a C++ library for high-performance finite element simulations of multiphysics, multiscale and multidomain problems. In this release, we introduce an additional intergrid transfer method for non-matching multiphysics coupling on the same domain, significantly optimize nearest-neighbor point searches and interface coupling utilities, extend the support for 2D and mixed-dimensional problems, and provide improved facilities for input/output and simulation serialization and restart. These advancements also propagate to the previously released modules of lifex specifically designed for cardiac modeling and simulation, namely lifex-fiber [Africa et al., BMC Bioinformatics (2023)], lifex-ep [Africa et al., BMC Bioinformatics (2023)] and lifex-cfd [Africa et al., Computer Physics Communications (2024)]. The changes introduced in this release aim at consolidating lifex's position as a valuable and versatile tool for the simulation of multiphysics systems. |
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100/2024 - 27/11/2024
Farenga, N.; Fresca, S.; Brivio, S.; Manzoni, A.
On latent dynamics learning in nonlinear reduced order modeling | Abstract | | In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality reduction problem, while constraining the latent state to evolve accordingly to an (unknown) dynamical system, namely a latent vector ordinary differential equation (ODE). A time-continuous setting is employed to derive error and stability estimates for the LDM approximation of the full order model (FOM) solution. We analyze the impact of using an explicit Runge-Kutta scheme in the time-discrete setting, and further explore the learnable setting where deep neural networks approximate the discrete LDM components, while providing a bounded approximation error with respect to the FOM. Moreover, we extend the concept of parameterized Neural ODE - recently proposed as a possible way to build data-driven dynamical systems with varying input parameters - to be a convolutional architecture, where the input parameters information is injected by means of an affine modulation mechanism, while designing a convolutional autoencoder neural network able to retain spatial-coherence, thus enhancing interpretability at the latent level. Numerical experiments, including the Burgers’ and the advection-reaction-diffusion equations, demonstrate the framework’s ability to obtain, in a multi-query context, a time-continuous approximation of the FOM solution, thus being able to query the LDM approximation at any given time instance while retaining a prescribed level of accuracy. Our findings highlight the remarkable potential of the proposed LDMs, representing a mathematically rigorous framework to enhance the accuracy and approximation capabilities of reduced order modeling for time-dependent parameterized PDEs. |
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99/2024 - 23/11/2024
Ragni, A.; Masci, C.; Paganoni, A. M.
Analysis of Higher Education Dropouts Dynamics through Multilevel Functional Decomposition of Recurrent Events in Counting Processes | Abstract | | This paper analyzes the dynamics of higher education dropouts through an innovative approach that integrates recurrent events modeling and point process theory with functional data analysis. We propose a novel methodology that extends existing frameworks to accommodate hierarchical data structures, demonstrating its potential through a simulation study. Using administrative data from student careers at Politecnico di Milano, we explore dropout patterns during the first year across different bachelor's degree programs and schools.
Specifically, we employ Cox-based recurrent event models, treating dropouts as repeated occurrences within both programs and schools. Additionally, we apply functional modeling of recurrent events and multilevel principal component analysis to disentangle latent effects associated with degree programs and schools, identifying critical periods of dropout risk and providing valuable insights for institutions seeking to implement strategies aimed at reducing dropout rates. |
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98/2024 - 14/11/2024
Castiglione, C.; Arnone, E.; Bernardi, M.; Farcomeni, A.; Sangalli, L.M.
PDE-regularised spatial quantile regression | Abstract | | We consider the problem of estimating the conditional quantiles of an unknown distribution from data gathered on a spatial domain. We propose a spatial quantile regression model with differential regularisation. The penalisation involves a partial differential equation defined over the considered spatial domain, that can display a complex geometry. Such regularisation permits, on one hand, to model complex anisotropy and non-stationarity patterns, possibly on the basis of problem-specific knowledge, and, on the other hand, to comply with the complex conformation of the spatial domain. We define an innovative functional Expectation-Maximisation algorithm, to estimate the unknown quantile surface. We moreover describe a suitable discretisation of the estimation problem, and investigate the theoretical properties of the resulting estimator. The performance of the proposed method is assessed by simulation studies, comparing with state-of-the-art techniques for spatial quantile regression. Finally, the considered model is applied to two real data analyses, the first concerning rainfall measurements in Switzerland and the second concerning sea surface conductivity data in the Gulf of Mexico. |
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