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 1253 products
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25/2024 - 03/06/2024
Enrico Ballini e Luca Formaggia e Alessio Fumagalli e Anna Scotti e Paolo Zunino
Application of Deep Learning Reduced-Order Modeling for Single-Phase Flow in Faulted Porous Media | Abstract | | We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach benefits from a mixed-dimensional framework that effectively manages the resulting non-conforming mesh. To streamline complex and repetitive calculations such as sensitivity analysis and solution of inverse problems, we utilize the Deep Learning Reduced Order Model (DL-ROM). This non-intrusive neural network-based technique is evaluated against the traditional Proper Orthogonal Decomposition (POD) method across various scenarios, demonstrating DL-ROM's capacity to expedite complex analyses with promising accuracy and efficiency. |
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22/2024 - 03/02/2024
Gatti, F.; de Falco, C.; Fois, M.; Formaggia, L.
A scalable well-balanced numerical scheme for a depth-integrated lava flow model | Abstract | | We propose a scalable well-balanced numerical method to efficiently solve a modified set of shallow water equations targeting the dynamics of lava flows. The governing equations are an extension of a depth-integrated model already available in the literature and proposed to model lava flows. Here, we consider the presence of vents that act as point sources in the mass and energy equations. Starting from a scheme developed in the framework of landslide simulation, we prove its capability to deal with lava flows. We show its excellent performances in terms of parallel scaling efficiency while maintaining good results in terms of accuracy. To verify the reliability of the proposed simulation tool, we first assess the accuracy and efficiency of the scheme on ideal scenarios. In particular, we investigate the well balancing property, we simulate benchmarks taken from the literature in the framework of lava flow simulations, and provide relevant scaling results for the parallel implementation of the method. Successively, we challenge the scheme on a real configuration taken from the available literature. |
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21/2024 - 02/26/2024
Caldana, M.; Antonietti P. F.; Dede' L.
Discovering Artificial Viscosity Models for Discontinuous Galerkin Approximation of Conservation Laws using Physics-Informed Machine Learning | Abstract | | Finite element-based high-order solvers of conservation laws offer large accuracy but face challenges near discontinuities due to the Gibbs phenomenon. Artificial viscosity is a popular and effective solution to this problem based on physical insight. In this work, we present a physics-informed machine learning algorithm to automate the discovery of artificial viscosity models in a non-supervised paradigm. The algorithm is inspired by reinforcement learning and trains a neural network acting cell-by-cell (the viscosity model) by minimizing a loss defined as the difference with respect to a reference solution thanks to automatic differentiation. This enables a dataset-free training procedure. We prove that the algorithm is effective by integrating it into a state-of-the-art Runge-Kutta discontinuous Galerkin solver. We showcase several numerical tests on scalar and vectorial problems, such as Burgers' and Euler's equations in one and two dimensions. Results demonstrate that the proposed approach trains a model that is able to outperform classical viscosity models. Moreover, we show that the learnt artificial viscosity model is able to generalize across different problems and parameters. |
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20/2024 - 02/22/2024
Torzoni, M.; Manzoni, A.; Mariani, S.
Structural health monitoring of civil structures: A diagnostic framework powered by deep metric learning | Abstract | | Recent advances in learning systems and sensor technology have enabled powerful strategies for autonomous data-driven damage detection in structural systems. This work proposes a novel method for the real-time localization of damage relying on a Siamese convolutional neural network. The method exploits a learnable mapping of raw vibration measurements onto a low-dimensional space, wherein damage locations can be easily identified. The mapping is learned in a supervised pairwise fashion exploiting labelled data, to induce a task-specific metric that allows to encode the damage position in the structure. Training data are generated through a reduced-order numerical model of the monitored structure. The damage position is then identified by performing a regression in the resulting low-dimensional features space. The proposed method does not require to define a-priori target classes and decision boundaries, thus requiring a limited amount of user-dependent assumptions. Results relevant to an L-shaped cantilever beam and a portal frame railway bridge demonstrate that the procedure can be effectively exploited for the purpose of damage localization. The method also proves to be insensitive to operational variability, measurement noise and modeling inaccuracies. |
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19/2024 - 02/22/2024
Torzoni, M.; Manzoni, A.; Mariani, S.
A multi-fidelity surrogate model for structural health monitoring exploiting model order reduction and artificial neural networks | Abstract | | Stochastic approaches to structural health monitoring (SHM) are often inevitably limited by computational constraints. For instance, for Markov chain Monte Carlo algorithms relying upon computationally expensive finite element models it is almost infeasible to sample the probability distribution of the structural state. To provide instead real-time procedures, this work proposes a non-intrusive surrogate modeling strategy, leveraging model order reduction and artificial neural networks. By relying upon a multi-fidelity (MF) framework, a composition of deep neural networks (DNNs) is devised to map damage and operational parameters onto time-dependent sensor recordings. Such an effective strategy is able to exploit datasets characterized by different fidelity levels without any prior assumption, allowing to blend a small high-fidelity (HF) dataset with a large low-fidelity (LF) dataset, ultimately alleviating the computational burden of supervised training while ensuring the accuracy of the approximated quantities of interest. The resulting surrogate model is made of an LF-DNN, which mimics sensor recordings in the undamaged condition, and of a long short-term memory HF-DNN, which adaptively refines the approximation with the effect of damage. An HF finite element model and an LF reduced order model are adopted offline to generate labeled training data of different fidelity, respectively in the presence or absence of a structural damage. Results relevant to an L-shaped cantilever beam and a portal frame railway bridge prove that the procedure efficiently provides remarkably accurate approximations, outperforming their single-fidelity counterparts. The capability of the MF-DNN to be exploited for SHM purposes is finally shown within an automated Bayesian procedure, aimed at updating the probability distribution of the structural state conditioned on sensor recordings, in the presence of operational variability and measurement noise. |
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17/2024 - 02/14/2024
Fois, M.; de Falco, C.; Formaggia, L.
A semi-conservative depth-averaged Material Point Method for fast flow-like landslides and mudflows | Abstract | | We present a two-dimensional semi-conservative variant of the depth averaged material point method (DAMPM) for modelling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier-Stokes equations with the inclusion of an appropriate bed friction model and material rheology, namely Voellmy and the depth-integrated Bingham viscoplastic stress model, respectively. After assessing the accuracy and performance of the proposed numerical method by means of several idealised benchmarks, we test its behaviour in a realistic scenario. |
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16/2024 - 02/12/2024
Domanin D. A.; Pegoraro M.; Trimarchi S.; Domanin M.; Secchi P.
Persistence diagrams for exploring the shape variability of abdominal aortic aneurysms | Abstract | | Abdominal Aortic Aneurysm consists of a permanent dilation in the abodminal portion of the aorta and, along with its associated pathologies like calcifications and intraluminal thrombi, is one of the most important pathologies of the circulatory system. The shape of the aorta is among the primary drivers for these health issues, with particular reference to all the characteristics which affects the hemodynamics. Starting from the computed tomography angiography of a patient, we propose to summarize such information using tools derived from Topological Data Analysis, obtaining persistence diagrams which describe the irregularities of the lumen of the aorta. We showcase the effectiveness of such shape-related descriptors with a series of supervised and unsupervised case studies. |
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14/2024 - 02/09/2024
Zappon, E.; Salvador, M.; Piersanti, R.; Regazzoni, F.; Dede', L.; Quarteroni, A.
An integrated heart-torso electromechanical model for the simulation of electrophysiological outputs accounting for myocardial deformation | Abstract | | When generating in-silico clinical electrophysiological outputs, such as electrocardiograms (ECGs) and body surface potential maps (BSPMs), mathematical models have relied on single physics, i.e. of the cardiac electrophysiology (EP), neglecting the role of the heart motion. Since the heart is the most powerful source of electrical activity in the human body, its motion dynamically shifts the position of the principal electrical sources in the torso, influencing electrical potential distribution and potentially altering the EP outputs. In this work, we propose a computational model for the simulation of ECGs and BSPMs by coupling a cardiac electromechanical model with a model that simulates the propagation of the EP signal in the torso, thanks to a flexible numerical approach, that simulates the torso domain deformation induced by the myocardial displacement. Our model accounts for the major mechano-electrical feedbacks, along with unidirectional displacement and potential couplings from the heart to the surrounding body. For the numerical discretization, we employ a versatile intergrid transfer operator that allows for the use of different Finite Element spaces to be used in the cardiac and torso domains. Our numerical results are obtained on a realistic 3D biventricular-torso geometry, and cover both cases of sinus rhythm and ventricular tachycardia (VT), solving both the electromechanical-torso model in dynamical domains, and the classical electrophysiology-torso model in static domains. By comparing standard 12-lead ECG and BSPMs, we highlight the non-negligible effects of the myocardial contraction on the EP-outputs, especially in pathological conditions, such as the VT.
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