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 1251 prodotti
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40/2024 - 30/05/2024
Carrara, D.; Regazzoni, F.; Pagani, S.
Implicit neural field reconstruction on complex shapes from scattered and noisy data | Abstract | | Reconstructing distributed physical quantities from scattered sensor data is a challenging task due to geometric and measurement uncertainties. We propose a novel machine learning based framework that allows to implicitly represent geometries solely from noisy surface points, by training a neural network model in a semi-supervised manner. We investigate different combinations of regularizing terms for the loss function, including a differential one based on the Eikonal equation, thus ensuring that the level set function approximates a signed distance function without the need for preprocessing data. This makes the method suitable for realistic, noise-corrupted, and sparse data. Furthermore, our approach leverages neural networks to predict distributed quantities defined on surfaces, while ensuring geometrical compatibility with the underlying implicit geometry representation. Our approach allows for accurate reconstruction of derived quantities such as surface gradients by relying on automatic differentiation tools. Comprehensive tests on synthetic data validate the method's efficacy, which demonstrate its potential for significant applications in healthcare. |
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39/2024 - 22/05/2024
Bartsch, J.; Buchwald, S.; Ciaramella, G.; Volkwein, S.
Reconstruction of unknown nonlienar operators in semilinear elliptic models using optimal inputs | Abstract | | Physical models often contain unknown functions and relations. The goal of our work is to answer the question of how one should excite or control a system under consideration in an appropriate way to be able to reconstruct an unknown nonlinear relation. To answer this question, we propose a greedy reconstruction algorithm within an offline-online strategy. We apply this strategy to a two-dimensional semilinear elliptic model. Our identification is based on the application of several space-dependent excitations (also called controls). These specific controls are designed by the algorithm in order to obtain a deeper insight into the underlying physical problem and a more precise reconstruction of the unknown relation. We perform numerical simulations that demonstrate the effectiveness of our approach which is not limited to the current type of equation. Since our algorithm provides not only a way to determine unknown operators by existing data but also protocols for new experiments, it is a holistic concept to tackle the problem of improving physical models. |
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38/2024 - 20/05/2024
Tonini, A., Regazzoni, F., Salvador, M., Dede', L., Scrofani, R., Fusini, L., Cogliati, C., Pontone, G., Vergara, C., Quarteroni, A.
Two new calibration techniques of lumped-parameter mathematical models for the cardiovascular system | Abstract | | Cardiocirculatory mathematical models serve as valuable tools for investigating physiological and pathological conditions of the circulatory system. To investigate the clinical condition of an individual, cardiocirculatory models need to be personalized
by means of calibration methods. In this study we propose a new calibration method for a lumped-parameter cardiocirculatory model. This calibration method utilizes the correlation matrix between parameters and model outputs to calibrate the latter according to data. We test this calibration method and its combination with L-BFGS-B (Limited
memory Broyden – Fletcher – Goldfarb – Shanno with Bound constraints) comparing them with the performances of L-BFGS-B alone. We show that the correlation matrix calibration method and the combined one effectively reduce the loss function of the associated
optimization problem. In the case of in silico generated data, we show that the two new calibration methods are robust with respect to the initial guess of parameters and to the presence of noise in the data. Notably, the correlation matrix calibration method achieves the best results in estimating the parameters in the case of noisy data
and it is faster than the combined calibration method and L-BFGS-B. Finally, we present real test case where the two new calibration methods yield results comparable to those obtained using L-BFGS-B in terms of minimizing the loss function and estimating the clinical data. This highlights the effectiveness of the new calibration methods for clinical applications. |
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37/2024 - 30/04/2024
Begu, B.; Panzeri, S.; Arnone, E.; Carey, M.; Sangalli, L.M.
A nonparametric penalized likelihood approach to density estimation of space-time point patterns | Abstract | |
In this work, we consider space-time point processes and study their continuous space-time evolution. We propose an innovative nonparametric methodology to estimate the unknown space-time density of the point pattern, or, equivalently, to estimate the intensity of an inhomogeneous space-time Poisson point process. The presented approach combines maximum likelihood estimation with roughness penalties, based on differential operators, defined over the spatial and temporal domains of interest. We first establish some important theoretical properties of the considered estimator, including its consistency. We then develop an efficient and flexible estimation procedure that leverages advanced numerical and computation techniques. Thanks to a discretization based on finite elements in space and B–splines in time, the proposed method can effectively capture complex multi-modal and strongly anisotropic spatio-temporal point patterns; moreover, these point patterns may be observed over planar or curved domains with non-trivial geometries, due to geographic constraints, such as coastal regions with complicated shorelines, or curved regions with complex orography. In addition to providing estimates, the method’s functionalities also include the introduction of appropriate uncertainty quantification tools. We thoroughly validate the proposed method, by means of simulation studies and applications to real-world data. The obtained results highlight significant advantages over state-of-the-art competing approaches.
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36/2024 - 29/04/2024
Torri, V.; Ercolanoni, M.; Bortolan, F.; Leoni, O.; Ieva, F.
A NLP-based semi-automatic identification system for delays in follow-up examinations: an Italian case study on clinical referrals | Abstract | | Background: This study aims to propose a semi-automatic method for monitoring the waiting times of follow-up examinations within the National Health System (NHS) in Italy, which is currently not possible to due the absence of the necessary structured information in the official databases.
Methods: A Natural Language Processing (NLP) based pipeline has been developed to extract the waiting time information from the text of referrals for follow-up examinations in the Lombardy Region. A manually annotated dataset of 10 000 referrals has been used to develop the pipeline and another manually annotated dataset of 10 000 referrals has been used to test its performance. Subsequently, the pipeline has been used to analyze all 12 million referrals prescribed in 2021 and performed by May 2022 in the Lombardy Region.
Results: The NLP-based pipeline exhibited high precision (0.999) and recall (0.973) in identifying waiting time information from referrals’ texts, with high accuracy in normalization (0.948-0.998). The overall reporting of timing indications in referrals’ texts for follow-up examinations was low (2%), showing notable variations across medical disciplines and types of prescribing physicians. Among the referrals reporting waiting times, 16% experienced delays (average delay = 19 days, standard deviation = 34 days), with significant differences observed across medical disciplines and geographical areas.
Conclusions: The use of NLP proved to be a valuable tool for assessing waiting times in follow-up examinations, which are particularly critical for the NHS due to the significant impact of chronic diseases, where follow-up exams are pivotal. Health authorities can exploit this tool to monitor the quality of NHS services and optimize resource allocation. |
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35/2024 - 22/04/2024
Botti, L.; Botti, M.; Di Pietro, D.A.; Massa; F.C.
Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressure | Abstract | | In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions that yield inf-sup stability as well as error estimates which distinguish the velocity- and pressure-related contributions to the error. We additionally identify the key properties under which the pressure-related contributions vanish in the estimate of the velocity,
thus leading to pressure-robustness. Several examples of existing and new schemes that fit into the framework are provided, and extensive numerical validation of the theoretical properties is provided. |
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34/2024 - 22/04/2024
Corti, M.
Exploring tau protein and amyloid-beta propagation: a sensitivity analysis of mathematical models based on biological data | Abstract | | Alzheimer's disease is the most common dementia worldwide. Its pathological development is well known to be connected with the accumulation of two toxic proteins: tau protein and amyloid-beta. Mathematical models and numerical simulations can predict the spreading patterns of misfolded proteins in this context. However, the calibration of the model parameters plays a crucial role in the final solution. In this work, we perform a sensitivity analysis of heterodimer and Fisher-Kolmogorov models to evaluate the impact of the equilibrium values of protein concentration on the solution patterns. We adopt advanced numerical methods such as the IMEX-DG method to accurately describe the propagating fronts in the propagation phenomena in a polygonal mesh of sagittal patient-specific brain geometry derived from magnetic resonance images. We calibrate the model parameters using biological measurements in the brain cortex for the tau protein and the amyloid-beta in Alzheimer's patients and controls. Finally, using the sensitivity analysis results, we discuss the applicability of both models in the correct simulation of the spreading of the two proteins. |
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32/2024 - 17/04/2024
Ziarelli, G.; Parolini, N.; Verani, M.
Learning epidemic trajectories through Kernel Operator Learning: from modelling to optimal control | Abstract | | Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consulted. In these complex epidemiological scenarios, machine learning architectures can play an important role, since they directly reconstruct data-driven models circumventing the specific modelling choices and the parameter calibration, typical of classical compartmental models. In this work, we discuss the efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics during epidemic outbreaks, where the transmission rate is ruled by an input strategy. In particular, we introduce two surrogate models, named KOL-m and KOL-$partial$, which reconstruct in two different ways the evolution of the epidemics. Moreover, we evaluate the generalization performances of the two approaches with different kernels, including the Neural Tangent Kernels, and compare them with a classical neural network model learning method. Employing synthetic but semi-realistic data, we show how the two introduced approaches are suitable for realizing fast and robust forecasts and scenario analyses, and how these approaches are competitive for determining optimal intervention strategies with respect to specific performance measures. |
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