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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67/2021 - 11/03/2021
Salvador, M.; Regazzoni, F.; Pagani, S.; Dede', L.; Trayanova, N.; Quarteroni, A.
The role of mechano-electric feedbacks and hemodynamic coupling in scar-related ventricular tachycardia | Abstract | | Mechano-electric feedbacks (MEFs), which model how mechanical stimuli are transduced into electrical signals, have received sparse investigation by considering electromechanical simulations in simplified scenarios. In this paper, we study the effects of different MEFs modeling choices for myocardial deformation and nonselective stretch-activated channels (SACs) in the monodomain equation. We perform numerical simulations during ventricular tachycardia (VT) by employing a biophysically detailed and anatomically accurate 3D electromechanical model for the left ventricle (LV) coupled with a 0D closed-loop model of the cardiocirculatory system. We model the electromechanical substrate responsible for scar-related VT with a distribution of infarct and peri-infarct zones. Our mathematical framework takes into account the hemodynamic effects of VT due to myocardial impairment and allows for the classification of their hemodynamic nature, which can be either stable or unstable. By combining electrophysiological, mechanical and hemodynamic models, we observe that all MEFs may alter the propagation of the action potential and the morphology of the VT. In particular, we notice that the presence of myocardial deformation in the monodomain equation may change the VT basis cycle length and the conduction velocity but do not affect the hemodynamic nature of the VT. Finally, nonselective SACs may affect wavefront stability, by possibly turning a hemodynamically stable VT into a hemodynamically unstable one and vice versa. |
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66/2021 - 11/03/2021
Antonietti, P.F.; Botti, M.; Mazzieri, I.
On mathematical and numerical modelling of multiphysics wave propagation with polygonal Discontinuous Galerkin methods | Abstract | | In this work we present discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic,
poro-elastic, and poro-elasto-acoustic materials. Wave ropagation is modeled by using either the elastodyanmics equation, in the elastic domain, the acoustics equations in the acoustic domain and the low-frequency Biot’s equations in the poro-elastic one.
The coupling between different models is realized by means of (physically consistent) transmission conditions, weakly imposed on the interface between the domains. For all models configuration, we introduce and analyse the PolydG semi-discrete formulation, which is then coupled with suitable time marching schemes. For the semi-discrete problem, we present the stability analysis and derive a-priori error estimates in a suitable energy norm. A wide set of verification tests with manufactured solutions are presented in order to validate the error analysis. Examples of physical interest are also shown to demonstrate the capability of the proposed methods. |
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65/2021 - 11/03/2021
Mazzieri, I.; Muhr, M.; Stupazzini, M.; Wohlmuth, B.
Elasto-acoustic modelling and simulation for the seismic response of structures: The case of the Tahtali dam in the 2020 Izmir earthquake | Abstract | | As a mean to assess the risk dam structures are exposed to during earthquakes, we employ an abstract mathematical, three dimensional, elasto-acoustic coupled wave-propagation model taking into account (i) the dam structure itself, embedded into (ii) its surrounding topography, (iii) different material soil layers, (iv) the seismic source as well as (v) the reservoir lake filled with water treated as an acoustic medium. As a case study for extensive numerical simulations we consider the magnitude 7 seismic event of the 30th of October 2020 taking place in the Icarian Sea (Greece) and the Tahtali dam around 30km from there (Turkey). A challenging task is to resolve the multiple length scales that are present due to the huge differences in size between the dam building structure and the area of interest, considered for the propagation of the earthquake. Interfaces between structures and highly non-conforming meshes on different scales are resolved by means of a discontinuous Galerkin approach. The seismic source is modeled using inversion data about the real fault plane. Ultimately, we perform a real data driven, multi-scale, full source-to-site, physics based simulation based on the discontinuous Galerkin spectral element method, which allows to precisely validate the ground motion experienced along the Tahtali dam, comparing the synthetic seismograms against actually observed ones. A comparison with a more classical computational method, using a plane wave with data from a deconvolved seismogram reading as an input, is discussed. |
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64/2021 - 10/22/2021
Clarotto, L; Allard, D.; Menafoglio, A.
A new class of alpha-transformations for the spatial analysis of Compositional Data | Abstract | | Georeferenced compositional data are prominent in many scientic fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of transformations, named the Isometric alpha-transformation (alpha-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation. It is shown that the ILR is the limit case of the alpha-IT as alpha tends to 0 and that alpha = 1 corresponds to a linear transformation of the data. Unlike the ILR, the proposed transformation accepts 0s in the compositions when alpha > 0. Maximum likelihood estimation of the parameter alpha is established. Prediction using kriging on alpha-IT transformed data is validated on synthetic spatial compositional data, using prdiction scores computed either in the geometry induced by the alpha-IT, or in the simplex. Application to land cover data shows that the relative superiority of the various approaches w.r.t. a prediction objective depends on whether the compositions contained any zero component. When all components are positive, the limit cases (ILR or linear transformations) are optimal for none of the considered metrics. An intermediate geometry, corresponding to the alpha-IT with maximum likelihood estimate, better describes the dataset in a geostatistical setting. When the amount of compositions with 0s is not negligible, some side-effects of the transformation gets amplied as alpha decreases, entailing poor kriging performances both within the alpha-IT geometry and for metrics in the simplex. |
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63/2021 - 10/22/2021
Rosafalco, L.; Torzoni, M.; Manzoni, A.; Mariani, S.; Corigliano, A.
Online structural health monitoring by model order reduction and deep learning algorithms | Abstract | | Within a structural health monitoring (SHM) framework, we propose a simulation-based classification strategy to move towards online damage localization. The procedure combines parametric Model Order Reduction (MOR) techniques and Fully Convolutional Networks (FCNs) to analyze raw vibration measurements recorded on the monitored structure. First, a dataset of possible structural responses under varying operational conditions is built through a physics-based model, allowing for a finite set of predefined damage scenarios. Then, the dataset is used for the offline training of the FCN. Because of the extremely large number of model evaluations required by the dataset construction, MOR techniques are employed to reduce the computational burden. The trained classifier is shown to be able to map unseen vibrational recordings, e.g. collected on-the-fly from sensors placed on the structure, to the actual damage state, thus providing information concerning the presence and also the location of damage. The proposed strategy has been validated by means of two case studies, concerning a 2D portal frame and a 3D portal frame railway bridge; MOR techniques have allowed us to respectively speed up the analyses about 30 and 420 times. For both the case studies, after training the classifier has attained an accuracy greater than 85%. |
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62/2021 - 10/14/2021
Lupo Pasini, M.; Burcul, M.; Reeve, S.; Eisenbach, M.; Perotto, S.
Fast and accurate predictions of total energy for solid solution alloys with graph convolutional neural networks | Abstract | | We use graph convolutional neural networks (GCNNs) to produce fast and accurate predictions of the total energy of solid solution binary alloys. GCNNs allow us to abstract the lattice structure of a solid material as a graph, whereby atoms are modeled as nodes and metallic bonds as edges. This representation naturally incorporates information about the structure of the material, thereby eliminating the need for computationally expensive data pre-processing which would be required with standard neural network (NN) approaches. We train GCNNs on ab-initio density functional theory (DFT) for copper-gold (CuAu) and iron-platinum (FePt) data that has been generated by running the LSMS-3 code, which implements a locally self-consistent multiple scattering method, on OLCF supercomputers Titan and Summit. GCNN outperforms the ab-initio DFT simulation by orders of magnitude in terms of computational time to produce the estimate of the total energy for a given atomic configuration of the lattice structure.
We compare the predictive performance of GCNN models against a standard NN such as dense feedforward multi-layer perceptron (MLP) by using the root-mean-squared errors to quantify the predictive quality of the deep learning (DL) models. We find that the attainable accuracy of GCNNs is at least an order of magnitude better than that of the MLP. |
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61/2021 - 09/27/2021
Buchwald, S.; Ciaramella, G.; Salomon, J.; Sugny, D.
A greedy reconstruction algorithm for the identification of spin distribution | Abstract | | We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in Nuclear Magnetic Resonace. The identification is based on the application of a number of constant control processes during a given time for which the final ensemble magnetization vector is measured. From these experimental data, we show that the identifiability of a piecewise constant approximation of the probability distribution is related to the invertibility of a matrix which depends on the different control protocols applied to the system.
The algorithm aims to design specific controls which ensure that this matrix is as far as possible from a singular matrix. Numerical simulations reveal the efficiency of this algorithm on different examples. A systematic comparison with respect to random constant pulses is done. |
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60/2021 - 09/27/2021
Rosafalco, L.; Manzoni, A.; Mariani, S.; Corigliano, A.
Fully convolutional networks for structural health monitoring through multivariate time series classification | Abstract | | We propose a novel approach to Structural Health Monitoring (SHM), aiming at the automatic identification of damage-sensitive features from data acquired through pervasive sensor systems. Damage detection and localization are formulated as classification problems, and tackled through Fully Convolutional Networks (FCNs). A supervised training of the proposed network architecture is performed on data extracted from numerical simulations of a physics-based model (playing the role of digital twin of the structure to be monitored) accounting for different damage scenarios. By relying on this simplified model of the structure, several load conditions are considered during the training phase of the FCN, whose architecture has been designed to deal with time series of different length. The training of the neural network is done before the monitoring system starts operating, thus enabling a real time damage classification. The numerical performances of the proposed strategy are assessed on a numerical benchmark case consisting of an eight-story shear building subjected to two load types, one of which modeling random vibrations due to low-energy seismicity. Measurement noise has been added to the responses of the structure to mimic the outputs of a real monitoring system. Extremely good classification capacities are shown: among the nine possible alternatives (represented by the healthy state and by a damage at any floor), damage is correctly classified in up to 95% of cases, thus showing the strong potential of the proposed approach in view of the application to real-life cases. |
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