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 1242 products
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27/2021 - 05/14/2021
Scimone, R.; Menafoglio, A.; Sangalli, L.M.; Secchi, P.
A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities | Abstract | | With the tools and perspective of Object Oriented Spatial Statistics, we analyze official daily data on mortality from all causes in the provinces and municipalities of Italy for the year 2020, the first of the COVID-19 pandemic. By comparison with mortality data from 2011 to 2019, we assess the local impact of the pandemic as perturbation factor of the natural spatio-temporal death process. For each Italian province, mortality data are represented by the densities of time of death in the year. Densities are regarded as functional data belonging to the Bayes space B^2 where we use functional-on-functional linear models to predict the expected mortality in 2020, based on mortality in previous years, and we compare predictions with actual observations to assess the impact of the pandemic. Through spatial downscaling of the provincial data down to the municipality level, we identify spatial clusters characterized by mortality densities anomalous with respect to those predicted based on mortality data of the nearby areas. This analysis pipeline could be extended to indexes different from death counts, measured at a granular spatio-temporal scale, and used as proxies for quantifying the local disruption generated by the pandemic. |
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26/2021 - 05/14/2021
Vigano, L.; Sollini, M.; Ieva, F.; Fiz, F.; Torzilli, G.
Chemotherapy-Associated Liver Injuries: Unmet Needs and New Insights for Surgical Oncologists | Abstract | | Chemotherapy-associated liver injuries (CALI) were the focus of several research studies some years ago when they were associated with modern treatments for colorectal metastases and operative outcomes of liver resection. An intensive, multidisciplinary commitment was designed to elucidate their pathogenesis, risk factors, clinical impact, diagnosis, and prevention. CALI are still part of our clinical practice and clinicians have further reasons to pursue CALI diagnosis.
This is mandatory to assess the effectiveness of any measure to reduce or prevent liver injuries. Second, diagnosis is needed in case of recurrent disease when patients require new chemotherapy lines and repeated surgery.
CALI are crucial to predict tolerance to treatment and operative risks. Finally, the identification of CALI is needed as long as they have some oncological impact. Even if not associated with prognosis, some studies highlighted an inverse relationship between CALI and response to chemotherapy (tumor regression is less evident in patients with severe injuries). |
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24/2021 - 04/26/2021
Regazzoni, F.; Chapelle, D.; Moireau, P.
Combining Data Assimilation and Machine Learning to build data-driven models for unknown long time dynamics - Applications in cardiovascular modeling | Abstract | | We propose a method to discover differential equations describing the long-term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast-scale. Our methodology is based on a synergetic combination of Data Assimilation (DA), used to estimate the parameters associated with the known fast-scale dynamics, and Machine Learning (ML), used to infer the laws underlying the slow-scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data-driven models obtained within the black-box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill-posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise-robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods. |
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25/2021 - 04/26/2021
Tenderini, R.; Pagani, S.; Quarteroni, A.; Deparis S.
PDE-aware deep learning for inverse problems in cardiac electrophysiology | Abstract | | In this work, we present a PDE-aware deep learning (DL) model, named Space-Time Reduced Basis Deep Neural Network (ST-RB-DNN), for the numerical solution to the Inverse Problem of Electrocardiography. The main feature of the proposed neural network (NN) is that it both leverages data availability and exploits the knowledge of a physically- based mathematical model, expressed by means of partial differential equations (PDEs), to carry out the task at hand. The goal is to estimate the epicardial potential field from measurements of the electric potential at a discrete set of points on the body surface. Such a problem has become central in biomedical research, providing the theoretical basis for Electrocardiographic Imaging (ECGI), but it is extremely hard to solve because of its ill-posedness. The employment of deep learning techniques in this context is made difficult by the low amount of clinical data at disposal (small data regime), as measuring cardiac potentials requires invasive procedures. Suitably exploiting the underlying physically- based mathematical model allowed to circumvent the data availability issue and led to the development of fast-training and low-complexity PDE-aware DL models. In particular, physical-awareness has been pursued by means of two elements: the projection of the epicardial potential onto a Space-Time Reduced subspace, spanned by the numerical solutions of the governing PDEs, and the inclusion of a tensorial Reduced Basis (RB) solver of the Forward Problem in the network architecture. Numerical tests have been conducted only on synthetic data, obtained via a Full Order Model (FOM) approximation of the problem at hand, and two variants of the model have been addressed. Both proved to be accurate, up to an average l1-norm relative error on epicardial activation maps of ? 3.5%, and both could be trained in ? 10 min. Nevertheless, some improvements, mostly concerning data generation, are necessary in order to bridge the gap with clinical applications. |
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23/2021 - 04/24/2021
Scimone, R.; Taormina, T.; Colosimo, B. M.; Grasso, M.; Menafoglio, A.; Secchi, P.
Statistical modeling and monitoring of geometrical deviations in complex shapes with application to Additive Manufacturing | Abstract | | The industrial development of new production processes like additive manufacturing (AM) is making available novel types of complex shapes that go beyond traditionally manufactured geometries and 2.5D free-form surfaces. New challenges must be faced to characterize, model and monitor the natural variability of such complex shapes, since previously proposed methods based on parametric models are not applicable. The present study proposes a methodology that applies to complex shapes represented in the form of triangulated meshes, which is the current standard for AM data format. The method combines a novel bi-directional way to model the deviation between the reconstructed geometry (e.g., via x-ray computed tomography) and the nominal geometry (i.e., the originating 3D model) with a profile monitoring approach for the detection of out-of-control shapes. A paradigmatic example consisting of an egg-shaped trabecular shell representative of real parts produced via AM is used to illustrate the methodology and to test its effectiveness in detecting real geometrical distortions. |
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22/2021 - 04/24/2021
Domanin, M.; Bennati, L.; Vergara, C.; Bissacco, D.; Malloggi, C.; Silani, V.; Parati, G.; Trimarchi, S.; Casana, R.
Fluid structure interaction analysis to stratify the behavior of different atheromatous carotid plaques | Abstract | | Objectives: Different plaque types could have different hemodynamic and structural behaviors in asymptomatic carotid stenosis (ACS), increasing the risk of instability.
Methods: The vessel lumen, the wall, and the geometries of three different types of carotid plaques, namely lipid (LP), fibrous (FP), and calcific (CP) were reconstructed starting with CTA images from 15 candidate patients for carotid revascularization with ACS >70%, in order to obtain 5 models for each type. Fluid structure interaction (FSI) analyses were performed to describe hemodynamic and structural behavior in different types of plaques by computing wall shear stresses (WSS), plaque displacements (D), von Mises stresses (VMS), and absorbed elastic energy (AEE) spatial distribution and their maximum-in-space values at the systolic peak, namely WSSsyst, Dsyst, VMSsyst and AEEsyst.
Results: WSSsyst resulted significantly lower in LP, whereas in FP we found intermediate values (+33%) and the highest WSSsyst (+157%) in CP. The highest values of Dsyst were observed in LP, with a different spatial distribution, being localized mainly in the inner region of the thin fibrous cap, at the shoulder of the stenosis, whereas for FP and CP the values were -250% and -480% lower, respectively. VMSsyst in the LP group was again localized to the inner region of the thin fibrous cap, whereas FP and CP had lower values, -150% and -400%, respectively, without spatial concentration of peak stresses. AEEsyst was determined to be focused at the fibrous cap, and capable of storing elevated values of energy due to the compliant nature of the inner core in LP, while lower values were found for FP and CP, -470% and -2240%, respectively.
Conclusions: Depending upon their nature, plaques store different amounts of mechanical energy. The deformation causes different distributions of internal forces inside the plaque, thus influencing vulnerability properties, especially for LP.
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21/2021 - 04/10/2021
Torti, A.; Galvani, M.; Menafoglio, A.; Secchi, P.; Vantini S.
A General Bi-clustering Algorithm for Hilbert Data: Analysis of the Lombardy Railway Service | Abstract | | A general and flexible bi-clustering algorithm for the analysis of Hilbert data is presented in the Object Oriented Data Analysis framework. The algorithm, called HC2 (i.e. Hilbert Cheng and Church), is a non-parametric method to bi-cluster Hilbert data indexed in a matrix structure.
The Cheng and Church approach is here extended to the general case of data embedded in a Hilbert space and then applied to the analysis of the regional railway service in the Lombardy region with the aim of identifying recurrent patterns in the passengers' daily access to trains and/or stations. The analysed data, modelled as multivariate functional data and time series, allows to measure both overcrowding and travel demand, providing useful insights to best handle the service. |
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20/2021 - 04/10/2021
Pasquale, A.; Ammar, A.; Falcó, A.; Perotto, S.; Cueto, E.; Duval, J.-L.; Chinesta, F.
A separated representation involving multiple time scales within the Proper Generalized Decomposition framework | Abstract | | Solutions of partial differential equations can exhibit multiple time scales. Standard discretization techniques are constrained to capture the finest scale to accurately predict the response of the system. In this paper, we provide an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors. The proposed methodology is based on a time-separated representation within the standard Proper Generalized Decomposition, where the time coordinate is transformed into a multi-dimensional time through new separated coordinates, each representing one scale, while continuity is ensured in the scale coupling. For instance, when considering two different time scales, the governing Partial Differential Equation is commuted into a nonlinear system that iterates between the so-called microtime and macrotime, so that the time coordinate can be viewed as a 2D time. The macroscale effects are taken into account by means of a finite element-based macro-discretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the time domain. The resulting separated representation allows us a very fine time discretization without impacting the computational efficiency. The proposed formulation is explored and numerically verified on thermal and elastodynamic problems. |
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