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 1239 products
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42/2023 - 05/11/2023
Tonini, A.; Vergara, C.; Regazzoni, F.; Dedè, L.; Scrofani, R.; Cogliati, C.; Quarteroni, A.
A mathematical model to assess the effects of COVID-19 on the cardiocirculatory system | Abstract | | Impaired cardiac function has been described as a frequent complication of COVID-19-related pneumonia. To investigate possible underlying mechanisms, we represented the cardiovascular system by means of a lumped-parameter 0D mathematical model. The model was calibrated using clinical data, recorded in 58 patients hospitalized for COVID-19-related pneumonia, to make it patient-specific and to compute model outputs of clinical interest related to the cardiocirculatory system. We assessed, for each patient with a successful calibration, the statistical reliability of model outputs estimating the uncertainty intervals. Then, we performed a statistical analysis to compare healthy ranges and mean values (over patients) of reliable model outputs to determine which were significantly altered in COVID-19-related pneumonia. Our results showed significant increases in right ventricular systolic pressure, diastolic and mean pulmonary arterial pressure, and capillary wedge pressure. Instead, physical quantities related to the systemic circulation were not significantly altered. Remarkably, statistical analyses made on raw clinical data, without the support of a mathematical model, were unable to detect the effects of COVID-19-related pneumonia, thus suggesting that the use of a calibrated 0D mathematical model to describe the cardiocirculatory system is an effective tool to investigate the impairments of the cardiocirculatory system associated with COVID-19. |
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41/2023 - 05/10/2023
Corti M.; Bonizzoni, F.; Antonietti, P.F.; Quarteroni, A.M.
Uncertainty Quantification for Fisher-Kolmogorov Equation on Graphs with Application to Patient-Specific Alzheimer Disease | Abstract | | The Fisher-Kolmogorov equation is a diffusion-reaction PDE that is used to model the accumulation of prionic proteins, which are responsible for many different neurological disorders. Likely, the most important and studied misfolded protein in literature is the Amyloid-beta, responsible for the onset of Alzheimer disease. Starting from medical images we construct a reduced-order model based on a graph brain connectome. The reaction coefficient of the proteins is modelled as a stochastic random field, taking into account all the many different underlying physical processes, which can hardly be measured. Its probability distribution is inferred by means of the Monte Carlo Markov Chain method applied to clinical data. The resulting model is patient-specific and can be employed for predicting the disease's future development. Forward uncertainty quantification techniques (Monte Carlo and sparse grid stochastic collocation) are applied with the aim of quantifying the impact of the variability of the reaction coefficient on the progression of protein accumulation within the next 20 years. |
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40/2023 - 05/06/2023
Ballini, E.; Chiappa, A.S.; Micheletti, S.
Reducing the Drag of a Bluff Body by Deep Reinforcement Learning | Abstract | | We present a deep reinforcement learning approach to a classical problem in fluid dynamics, i.e., the reduction of the drag of a bluff body. We cast the problem as a discrete-time control with continuous action space: at each time step, an autonomous agent can set the flow rate of two jets of fluid, positioned at the back of the body. The agent, trained with Proximal Policy Optimization, learns an effective strategy to make the jets interact with the vortexes of the wake, thus reducing the drag. To tackle the computational complexity of the fluid dynamics simulations, which would make the training procedure prohibitively expensive, we train the agent on a coarse discretization of the domain. We provide numerical evidence that a policy trained in this approximate environment still retains good performance when carried over to a denser mesh. Our simulations show a considerable drag reduction with a consequent saving of total power, defined as the sum of the power spent by the control system and of the power of the drag force, amounting to 40% when compared to simulations with the reference bluff body without any jet. Finally, we qualitatively investigate the control policy learnt by the neural network. We can observe that it achieves the drag reduction by learning the frequency of formation of the vortexes and activating the jets accordingly, thus blowing them away off the rear body surface. |
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39/2023 - 05/02/2023
Riccobelli, D.; Al-Terke, H. H.; Laaksonen, P.; Metrangolo, P.; Paananen, A.; Ras, R. H. A.; Ciarletta, P.; Vella, D.
Flattened and wrinkled encapsulated droplets: Shape-morphing induced by gravity and evaporation | Abstract | | We report surprising morphological changes of suspension droplets (containing class II hydrophobin protein HFBI from Trichoderma reesei in water) as they evaporate with a contact line pinned on a rigid solid substrate. Both pendant and sessile droplets display the formation of an encapsulating elastic film as the bulk concentration of solute reaches a critical value during evaporation, but the morphology of the droplet varies significantly: for sessile droplets, the elastic film ultimately crumples in a nearly flattened area close to the apex while in pendant droplets, circumferential wrinkling occurs close to the contact line. These different morphologies are understood through a gravito-elasto-capillary model that predicts the droplet morphology and the onset of shape changes, as well as showing that the influence of the direction of gravity remains crucial even for very small droplets (where the effect of gravity can normally be neglected). The results pave the way to control droplet shape in several engineering and biomedical applications. |
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38/2023 - 04/29/2023
Africa, P. C.; Fumagalli, I.; Bucelli, M.; Zingaro, A.; Fedele, M.; Dede', L.; Quarteroni, A.
lifex-cfd: an open-source computational fluid dynamics solver for cardiovascular applications | Abstract | | Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and
dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the
strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we
present lifex-cfd: an open-source CFD solver for cardiovascular simulations based on the lifex finite element
library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both
physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving
cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of
the underlying mathematical formulation, numerical discretization, implementation details and instructions for
use of lifex-cfd. The code has been verified through rigorous convergence analyses, and we show its almost
ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented
through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow
regimes. The lifex-cfd source code is available under the LGPLv3 license, to ensure its accessibility and
transparency to the scientific community, and to facilitate collaboration and further developments. |
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37/2023 - 04/29/2023
Regazzoni, F.; Pagani, S.; Salvador, M.; Dede’, L.; Quarteroni, A.
Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes | Abstract | | Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to yield predictions through the numerical approximation of high-dimensional systems of differential equations, thus calling for large-scale parallel computing platforms and requiring large computational costs. Data-driven approaches, instead, enable the description of systems evolution in low-dimensional latent spaces, by leveraging dimensionality reduction and deep learning algorithms. We propose a novel architecture, named Latent Dynamics Network (LDNet), which is able to discover low-dimensional intrinsic dynamics of possibly non-Markovian dynamical systems, thus predicting the time evolution of space-dependent fields in response to external inputs. Unlike popular approaches, in which the latent representation of the solution manifold is learned by means of auto-encoders that map a high-dimensional discretization of the system state into itself, LDNets automatically discover a low-dimensional manifold while learning the latent dynamics, without ever operating in the high-dimensional space. Furthermore, LDNets are meshless algorithms that do not reconstruct the output on a predetermined grid of points, but rather at any point of the domain, thus enabling weight-sharing across query-points. These features make LDNets lightweight and easy-to-train, with excellent accuracy and generalization properties, even in time-extrapolation regimes. We validate our method on several test cases and we show that, for a challenging highly-nonlinear problem, LDNets outperform state-of-the-art methods in terms of accuracy (normalized error 5 times smaller), by employing a dramatically smaller number of trainable parameters (more than 10 times fewer). |
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35/2023 - 04/23/2023
Ferrari, L.; Manzi, G.; Micheletti, A.; Nicolussi, F.; Salini, S.
Pandemic Data Quality Modelling: A Bayesian Approach | Abstract | | When pandemics like COVID-19 spread around the world, the rapidly evolving situation compels officials and executives to take prompt decisions and adapt policies depending on the current state of the disease. In this context, it is crucial for policymakers to have always a firm grasp on what is the current state of the pandemic, and to envision how the number of infections and possible deaths is going to evolve over the next weeks. However, as in many other situations involving compulsory registration of sensitive data from multiple collectors, cases might be reported with errors, often with delays deferring an up-to-date view of the state of things. Errors in collecting new cases affect the overall mortality, resulting in excess deaths reported by official statistics only months later. In this paper, we provide tools for evaluating the quality of pandemic mortality data. We accomplish this through a Bayesian approach accounting for the excess mortality pandemics might bring with respect to the normal level of mortality in the population. |
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34/2023 - 04/23/2023
Caldana, M.; Antonietti, P. F.; Dede', L.
A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs | Abstract | | Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most severe limitation of AMG methods is the dependence on parameters that require to be fine-tuned. In particular, the strong threshold parameter is the most relevant since it stands at the basis of the construction of successively coarser grids needed by the AMG methods. We introduce a novel Deep Learning algorithm that minimizes the computational cost of the AMG method when used as a finite element solver. We show that our algorithm requires minimal changes to any existing code. The proposed Artificial Neural Network (ANN) tunes the value of the strong threshold parameter by interpreting the sparse matrix of the linear system as a black-and-white image and exploiting a pooling operator to transform it into a small multi-channel image. We experimentally prove that the pooling successfully reduces the computational cost of processing a large sparse matrix and preserves the features needed for the regression task at hand. We train the proposed algorithm on a large dataset containing problems with a highly heterogeneous diffusion coefficient defined in different three-dimensional geometries and discretized with unstructured grids and linear elasticity problems with a highly heterogeneous Young's modulus. When tested on problems with coefficients or geometries not present in the training dataset, our approach reduces the computational time by up to 30%. |
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