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 1287 products
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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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59/2021 - 09/27/2021
Stella, S.; Regazzoni, F.; Vergara, C.; Dede', L.; Quarteroni, A.
A fast cardiac electromechanics model coupling the Eikonal and the nonlinear mechanics equations | Abstract | | We present a new model of human cardiac electromechanics for the left ventricle where electrophysiology is described by a Reaction-Eikonal model and which enables an off-line resolution of the reaction model, thus entailing a big saving of computational time. Subcellular dynamics is coupled with a model of tissue mechanics, which is in turn coupled with a windkessel model for blood circulation. Our numerical results show that the proposed model is able to provide a physiological response to changes in certain variables (end-diastolic volume, total peripheral resistance, contractility). We also show that our model is able to reproduce with high accuracy (and with a considerably lower computational time) the results that we would obtain if the monodomain model should be used in place of the Eikonal model. |
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58/2021 - 08/25/2021
Tassi, T., Zingaro, A., Dede', L.
Enhancing numerical stabilization methods for advection dominated differential problems by Machine Learning algorithms | Abstract | | In this work, we propose a residual-based stabilization method for advection dominated differential problems enhanced by artificial neural networks. Specifically, we consider the Streamline Upwind Petrov-Galerkin stabilization method and we employ neural networks to compute an optimal form of the stabilization parameter on which the method relies. We train the neural network on a dataset generated by repeatedly solving an optimization problem, by minimizing the distance between the numerical solution and the exact one for different parametrizations of problem data and setting of the numerical scheme. The trained network is later used to predict the optimal stabilization for any given configuration and to be readily used ``online" for any new configuration of the problem. 1D and 2D numerical tests show that our novel approach leads to more accurate solutions than the standard approaches for the problem under consideration. |
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57/2021 - 08/24/2021
Roberto Piersanti, Francesco Regazzoni, Matteo Salvador, Antonio F. Corno, Luca Dede', Christian Vergara, Alfio Quarteroni
3D-0D closed-loop model for the simulation of cardiac biventricular electromechanics | Abstract | | Two crucial factors for accurate numerical simulations of cardiac electromechanics, which are also essential to reproduce the synchronous activity of the heart, are: i) accounting for the interaction between the heart and the circulatory system that determines pressures and volumes loads in the heart chambers; ii) reconstructing the muscular fiber architecture that drives the electrophysiology signal and the myocardium contraction. In this work, we present a 3D biventricular electromechanical model coupled with a 0D closed-loop model of the whole cardiovascular system that addresses the two former crucial factors. With this aim, we introduce a boundary condition for the mechanical problem that accounts for the neglected part of the domain located on top of the biventricular basal plane and that is consistent with the principles of momentum and energy conservation. We also discuss in detail the coupling conditions that stand behind the 3D and the 0D models. We perform electromechanical simulations in physiological conditions using the 3D-0D model and we show that our results match the experimental data of relevant mechanical biomarkers available in literature. Furthermore, we investigate different arrangements in cross-fibers active contraction. We prove that an active tension along the sheet direction counteracts the myofiber contraction, while the one along the sheet-normal direction enhances the cardiac work. Finally, several myofiber architectures are analysed. We show that a different fiber field in the septal area and in the transmural wall effect the pumping functionality of the left ventricle. |
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