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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83/2021 - 12/15/2021
Colasuonno, F.; Ferrari F.; Gervasio, P.; Quarteroni, A.
Some evaluations of the fractional p-Laplace operator on radial functions | Abstract | | We face a rigidity problem for the fractional p-Laplace operator to extend to this new framework some tools useful for the linear case. It is known that (-Delta)^s (1-bar xbar ^2)^s_+ and -Delta_p (1-bar x bar^(p/(p-1))) are constant functions in (-1,1) for fixed p and s. We evaluated (-Delta_p)^s(1-bar x bar^(p/(p-1)))^s proving that it is not constant in (-1,1) for some p in (1,+infty) and s in (0,1). This conclusion is obtained numerically thanks to the use of very accurate Gaussian numerical quadrature formulas. |
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82/2021 - 12/02/2021
Massi, M.C.; Ieva, F.
Learning Signal Representations for EEG Cross-Subject Channel Selection and Trial Classification | Abstract | | EEG is a non-invasive powerful system that finds applications in several domains and research areas. Most EEG systems are multi-channel in nature, but multiple channels might include noisy and redundant information and increase computational times of automated EEG decoding algorithms. To reduce the signal-to-noise ratio, improve accuracy and reduce computational time, one may combine channel selection with feature extraction and dimensionality reduction. However, as EEG signals present high inter-subject variability, we introduce a novel algorithm for subject-independent channel selection through representation learning of EEG recordings. The algorithm exploits channel-specific 1D-CNNs as supervised feature extractors to maximize class separability and reduces a high dimensional multi-channel signal into a unique 1-Dimensional representation from which it selects the most relevant channels for classification. The algorithm can be transferred to new signals from new subjects and obtain novel highly informative trial vectors of controlled dimensionality to be fed to any kind of classifier. |
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81/2021 - 12/02/2021
Massi, M.C.; Gasperoni, F.; Ieva, F.; Paganoni, A.
Feature Selection for Imbalanced Data with Deep Sparse Autoencoders Ensemble | Abstract | | Class imbalance is a common issue in many domain applications of learning algorithms. Oftentimes, in the same domains it is much more relevant to correctly classify and profile minority class observations. This need can be addressed by Feature Selection (FS), that offers several further advantages, s.a. decreasing computational costs, aiding inference and interpretability. However, traditional FS techniques may become sub-optimal in the presence of strongly imbalanced data. To achieve FS advantages in this setting, we propose a filtering FS algorithm ranking feature importance on the basis of the Reconstruction Error of a Deep Sparse AutoEncoders Ensemble (DSAEE). We use each DSAE trained only on majority class to reconstruct both classes. From the analysis of the aggregated Reconstruction Error, we determine the
features where the minority class presents a different distribution of values w.r.t. the overrepresented one, thus identifying the most relevant features to discriminate between the two. We empirically demonstrate the efficacy of our algorithm in several experiments, both simulated and on high-dimensional datasets of varying sample size, showcasing its capability to select relevant and generalizable features to profile and classify minority class, outperforming other benchmark FS methods. We also briefly present a real application in radiogenomics, where the methodology was applied successfully. |
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80/2021 - 12/02/2021
Sollini, M., Bartoli, F., Cavinato, L., Ieva, F., Ragni, A., Marciano, A., Zanca, R., Galli, L., Paiar, F., Pasqualetti , F. and Erba P. A.
[18F]FMCH PET/CT biomarkers and similarity analysis to refine the definition of oligometastatic prostate cancer | Abstract | | Background:The role of image-derived biomarkers in recurrent oligometastatic Prostate Cancer (PCa) is unexplored. This paper aimed to evaluate [18F]FMCH PET/CT radiomic analysis in patients with recurrent PCa after primary radical therapy. Specifically, we tested intra-patient lesions similarity in oligometastatic and plurimetastatic PCa, comparing the two most used definitions of oligometastatic disease.Methods:PCa patients eligible for [18F]FMCH PET/CT presenting biochemical failure after first-line curative treat-ments were invited to participate in this prospective observational trial. PET/CT images of 92 patients were visually and quantitatively analyzed. Each patient was classified as oligometastatic or plurimetastatic according to the total number of detected lesions (up to 3 and up to 5 or > 3 and > 5, respectively). Univariate and intra-patient lesions’ similarity analysis were performed.Results: [18F]FMCH PET/CT identified 370 lesions, anatomically classified as regional lymph nodes and distant metastases. Thirty-eight and 54 patients were designed oligometastatic and plurimetastatic, respectively, using a 3-lesion threshold. The number of oligometastic scaled up to 60 patients (thus 32 plurimetastatic patients) with a 5-lesion threshold. Similarity analysis showed high lesions’ heterogeneity. Grouping patients according to the number of metastases, patients with oligometastatic PCa defined with a 5-lesion threshold presented lesions heterogene-ity comparable to plurimetastic patients. Lesions within patients having a limited tumor burden as defined by three lesions were characterized by less heterogeneity.Conclusions:We found a comparable heterogeneity between patients with up to five lesions and plurimetastic patients, while patients with up to three lesions were less heterogeneous than plurimetastatic patients, featuring dif-ferent cells phenotypes in the two groups. Our results supported the use of a 3-lesion threshold to define oligometa-static PCa. |
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79/2021 - 12/02/2021
Ferraccioli, F.; Sangalli, L.M.; Finos, L.
Some first inferential tools for spatial regression with differential regularization | Abstract | | Spatial regression with differential regularization is an innovative approach at the crossroad between functional data analysis and spatial data analysis. These models have been shown to be numerically efficient and capable to handle complex applied problems. On the other hand, their theoretical properties are still largely unexplored. Here we consider the discrete estimators in spatial regression models with differential regularization, obtained after numerical discretization, using an expansion on a finite element basis. We study the consistency and the asymptotic normality of these discrete estimators. We also propose a nonparametric test procedure for the linear part of the models, based on random sign-flipping of the score components. The test exploits an appropriate decomposition of the smoothing matrix, in order to reduce the effect of the spatial dependence, without any parametric assumption on the form of the correlation structure. The proposed test is shown to be superior to parametric alternatives. |
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78/2021 - 12/02/2021
Bucelli, M.; Dede', L.; Quarteroni, A.; Vergara, C.
Partitioned and monolithic algorithms for the numerical solution of cardiac fluid-structure interaction | Abstract | | We review and compare different fluid-structure interaction (FSI) numerical methods in the context of heart modeling, aiming at assessing their computational efficiency for cardiac numerical simulations and selecting the most appropriate method for heart FSI. Blood dynamics within the human heart is characterized by active muscular action, during both contraction and relaxation phases of the heartbeat. The efficient solution of the FSI problem in this context is challenging, due to the added-mass effect (caused by the comparable densities of fluid and solid, typical of biomechanics) and to the complexity, nonlinearity and anisotropy of cardiac consitutive laws. In this work, we review existing numerical coupling schemes for FSI in the two classes of strongly-coupled partitioned and monolithic schemes. The schemes are compared on numerical tests that mimic the flow regime characterizing the heartbeat in a human ventricle, during both systole and diastole. Active mechanics is treated in both the active stress and active strain frameworks. Computational costs suggest the use of a monolithic method. We employ it to simulate a full heartbeat of a human ventricle, showing how it allows to efficiently obtain physiologically meaningful results. |
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77/2021 - 11/28/2021
Guo, M.; Manzoni, A.; Amendt, M.; Conti, P.; Hesthaven, J.S.
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities | Abstract | | Highly accurate numerical or physical experiments are often very time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide satisfactory model results. Multi-fidelity methods deal with such problems by incorporating information from other sources, which are ideally well-correlated with the high-fidelity data, but can be obtained at a lower cost. By leveraging correlations between different data sets, multi-fidelity methods often yield superior generalization when compared to models based solely on a small amount of high fidelity data. In the current work, we present the use of artificial neural networks applied to multi- fidelity regression problems. By elaborating a few existing approaches, we propose new neural network architectures for multi-fidelity regression. The introduced models are compared against a traditional multi- fidelity regression scheme - co-kriging. A collection of artificial benchmarks are presented to measure the performance of the analyzed models. The results show that cross-validation in combination with Bayesian optimization leads to neural network models that outperform the co-kriging scheme. Additionally, we show an application of multi-fidelity regression to an engineering problem. The propagation of a pressure wave into an acoustic horn with parametrized shape and frequency is considered, and the index of reflection intensity is approximated using the proposed multi-fidelity models. A finite element, full-order model and a reduced-order model built through the reduced basis method are adopted as the high- and low-fidelity, respectively. It is shown that the multi-fidelity neural networks return outputs that achieve a comparable accuracy to those from the expensive, full-order model, using only very few full-order evaluations combined with a larger amount of inaccurate but cheap evaluations of the reduced order model. |
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76/2021 - 11/28/2021
Ponti, L.; Perotto, S.; Sangalli, L.M.
A PDE-regularized smoothing method for space-time data over manifolds with application to medical data | Abstract | | We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold.
The proposed approach consists of a regression model completed with a regularizing term based on the heat equation.
The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm.
This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with
massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool
in practical contexts by dealing with neuroimaging and hemodynamic data. |
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