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
-
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. |
-
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. |
-
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.
|
-
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. |
-
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. |
-
19/2021 - 03/31/2021
Gillard, M.; Benacchio, T.
FT-GCR: a fault-tolerant generalized conjugate residual elliptic solver | Abstract | | With the steady advance of high performance computing systems
featuring smaller and smaller hardware components, the systems and
algorithms used for numerical simulations increasingly contend with
disruptions caused by hardware failures and bit-levels misrepresenta-
tions of computing data. In numerical frameworks exploiting massive
processing power, the solution of linear systems often represents the
most computationally intensive component. Given the large amount
of repeated operations involved, iterative solvers are particularly vulnerable to bit-flips.
A new method named FT-GCR is proposed here that supplies the
preconditioned Generalized Conjugate Residual Krylov solver with
detection of, and recovery from, soft faults. The algorithm tests on the monotonic decrease of the residual norm and, upon failure, restarts
the iteration within the local Krylov space. Numerical experiments
on the solution of an elliptic problem arising from a stationary flow
over an isolated hill on the sphere show the skill of the method in
addressing bit-flips on a range of grid sizes and data loss scenarios,
with best returns and detection rates obtained for larger corruption
events. The simplicity of the method makes it easily extendable to
other solvers and an ideal candidate for algorithmic fault tolerance
within integrated model resilience strategies. |
-
18/2021 - 03/31/2021
Gigante, G.; Vergara, C.
On the choice of interface parameters in Robin-Robin loosely coupled schemes for fluid-structure interaction | Abstract | | We consider two loosely-coupled schemes for the solution of the fluid-structure interaction problem in presence of large added mass effect. In particular, we introduce the Robin-Robin and Robin-Neumann explicit schemes where suitable interface conditions of Robin type are used. For the estimate of interface Robin parameters which guarantee stability of the numerical solution, we propose to optimize the reduction factor of the corresponding strongly-coupled (implicit) scheme, by means of the Optimized Schwarz method. To check the suitabilty of our proposals, we show numerical results both in an ideal cylindrical domain and in a real human carotid. |
-
17/2021 - 03/31/2021
Chew, R.; Benacchio, T.; Hastermann, G.; Klein, R.
Balanced data assimilation with a blended numerical model | Abstract | | A challenge arising from the local Bayesian assimilation of data in an atmospheric flow simulation is the imbalances it may introduce. Fast-mode imbalances of the order of the slower dynamics can be negated by employing a blended numerical model with seamless access to the compressible and the soundproof pseudo-incompressible dynamics. Here, the blended modelling strategy by Benacchio et al. (2014) is upgraded in an advanced numerical framework and extended with a Bayesian local ensemble data assimilation method. Upon assimilation of data, the model configuration is switched to the pseudo-incompressible regime for one time-step. After that, the model configuration is switched back to the compressible model for the duration of the assimilation window. The switching between model regimes is repeated for each subsequent assimilation window. An improved blending strategy ensures that a single time-step in the pseudo-incompressible regime is sufficient to filter imbalances. This improvement is based on three innovations: (i) the association of pressure fields computed at different stages of the numerical integration with actual time levels; (ii) a conversion of pressure-related variables between the model regimes derived from low Mach number asymptotics; and (iii) a judicious selection of the pressure variables used in converting numerical model states when a switch of models occurs. Travelling vortex and bubble convection experiments show that the imbalance arising from assimilation of the momentum fields can be eliminated by using this blended model, thereby achieving balanced analysis fields. The leftover imbalance in the thermodynamics can be quantified by scale analysis. |
|
