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 1256 products
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17/2025 - 04/04/2025
Botti, M.; Mascotto, L.
Sobolev--Poincaré inequalities for piecewise $W^{1,p}$ functions over general polytopic meshes | Abstract | | We establish Sobolev-Poincaré inequalities for piecewise $W^{1,p}$ functions over sequences of fairly general polytopic (thence also shape-regular simplicial and Cartesian) meshes in any dimension; amongst others, they cover the case of standard Poincaré inequalities for piecewise $W^{1,p}$ functions and can be useful in the analysis of nonconforming finite element discretizations of nonlinear problems. Crucial tools in their derivation are novel Sobolev-trace inequalities and Babuska-Aziz inequalities with mixed boundary conditions. We provide estimates that are constant free, i.e., that are fully explicit with respect to the geometric properties of the domain and the underlying sequence of polytopic meshes. |
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15/2025 - 03/14/2025
Fois, M.; de Falco, C.; Formaggia L.
Efficient particle generation for depth-averaged and fully 3D MPM using TIFF image data | Abstract | | In this work, we present a comprehensive framework for the generation and efficient management of particles in both fully three-dimensional (3D) and depth-averaged Material Point Method (DAMPM) simulations. Our approach leverages TIFF image data to construct initial conditions for large-scale geophysical flows, with a primary focus on landslide modeling. We describe the algorithms developed for particle initialization, distribution, and tracking, ensuring consistency and computational efficiency across different MPM formulations. The proposed methods enable accurate representation of complex topographies while maintaining numerical stability and adaptability to diverse material behaviors. Although the primary application is landslide simulation, the methodologies outlined are broadly applicable to other fields involving granular flows, fluid-structure interactions, and large-deformation processes. Performance evaluations demonstrate the efficiency and robustness of our approach, highlighting its potential for advancing high-fidelity simulations in geomechanics and beyond. |
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13/2025 - 02/28/2025
Scimone, R.; Menafoglio, A.; Secchi, P.
Estimating Non-Stationarity in Spatial Processes: an approach based on Random Domain Decomposition | Abstract | | The present work addresses the problem of flexible and efficient parameter estimation for non-stationary Gaussian random fields. This problem is crucial to enable modeling and stochastic simulation of complex natural phenomena in the Earth Sciences. Building on the non-stationary Matérn model of Paciorek and Schervish (2006), we propose a novel computational method that leverages random and repeated domain partitions to construct locally stationary estimates. Unlike existing approaches that rely on fixed grids of knots, our method employs a bagging-type strategy to mitigate the influence of domain decompositions in a divide-and-conquer fashion. This results in more robust and adaptive estimations, overcoming key limitations of traditional methods. Through extensive simulations and a real case study, we demonstrate that while fixed grids noticeably impact the final estimated models, our approach produces grid-free estimations, thanks to the additional source of randomness introduced by the aleatory partitions of the domain. |
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14/2025 - 02/28/2025
Nicolussi, F.; Masci, C.
Stratified Multilevel Graphical Models: Examining Gender Dynamics in Education | Abstract | | This study proposes a methodological approach to investigate gender disparities in education, particularly focusing on the schooling phase and its influence on career trajectories. The research applies multilevel linear models to analyse student performance concerning various factors, with a specific emphasis on gender-specific outcomes.
The study aims to identify and test context-specific independencies that may impact educational disparities between genders. The methodology includes the introduction of supplementary parameters in multilevel models to capture and examine these independencies. Furthermore, the research proposes encoding these novel relationships in graphical models, specifically stratified chain graph models, to visualize and generalize the complex dependencies among covariates, random effects, and gender influences on educational outcomes. |
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12/2025 - 02/26/2025
Alessandro Andrea Zecchi, Claudio Sanavio, Simona Perotto e Sauro Succi
Improved amplitude amplification strategies for the quantum simulation of classical transport problems | Abstract | | The quantum simulation of classical fluids often involves the use of probabilistic algorithms that encode the result of the dynamics in the form of the amplitude of the selected quantum state. In most cases, however, the amplitude probability is too low to allow an efficient use of these algorithms, thereby hindering the practical viability of the quantum simulation. The oblivious amplitude amplification algorithm is often presented as a solution to this problem, but to no avail for most classical problems, since its applicability is limited to unitary dynamics. In this paper, we show analytically that oblivious amplitude amplification when applied to non-unitary dynamics leads to a distortion of the quantum state and to an accompanying error in the quantum update. We provide an analytical upper bound of such error as a function of the degree of non-unitarity of the dynamics and we test it against a quantum simulation of an advection-diffusion-reaction equation, a transport problem of major relevance in science and engineering. Finally, we also propose an amplification strategy that helps mitigate the distortion error, while still securing an enhanced success probability. |
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11/2025 - 02/19/2025
Tonini, A.; Dede', L.
Enhanched uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems | Abstract | | Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in
real-time. In the Bayesian framework, variational autoencoders, a specialized type of neural network, enable the estimation of model
parameters and their distribution based on observational data allowing to perform real-time inverse uncertainty quantification. In this
work, we build upon existing research [Goh, H. et al., Proceedings of Machine Learning Research, 2022] by proposing a novel loss
function to train variational autoencoders for Bayesian inverse problems. When the forward map is affine, we provide a theoretical
proof of the convergence of the latent states of variational autoencoders to the posterior distribution of the model parameters. We
validate this theoretical result through numerical tests and we compare the proposed variational autoencoder with the existing one in the literature. Finally, we test the proposed variational autoencoder on the Laplace equation. |
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10/2025 - 02/13/2025
Botti, M.; Mascotto, L.; Vacca, G.; Visinoni, M.
Stability and interpolation estimates of Hellinger-Reissner virtual element spaces | Abstract | | We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme. We further investigate numerically the behaviour of the constants appearing in the stability estimates on sequences of badly-shaped polytopes and for increasing degree of accuracy. |
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09/2025 - 02/03/2025
Quarteroni, A.; Gervasio, P.; Regazzoni, F.
Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning | Abstract | | Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding of the problem at hand, subsequent mathematical formulation, and numerical approximation. Data-driven models instead aim to extract relations between input and output data without arguing any causality principle underlining the available data distribution. In recent years, data-driven models have been rapidly developed and popularized. Such a diffusion has been triggered by a huge availability of data (the so-called big data), an increasingly cheap computing power, and the development of powerful machine learning algorithms. SciML leverages the physical awareness of physics-based models and, at the same time, the efficiency of data-driven algorithms. With SciML, we can inject physics and mathematical knowledge into machine learning algorithms. Yet, we can rely on data-driven algorithms’ capability to discover complex and non-linear patterns from data and improve the descriptive capacity of physics-based models. After recalling the mathematical foundations of digital modelling and machine learning algorithms, and presenting the most popular machine learning architectures, we discuss the great potential of a broad variety of SciML strategies in solving complex problems governed by partial differential equations. Finally, we illustrate the successful application of SciML to the simulation of the human cardiac function, a field of significant socio-economic importance that poses numerous challenges on both the mathematical and computational fronts. The corresponding mathematical model is a complex system of non-linear ordinary and partial differential equations describing the electromechanics, valve dynamics, blood circulation, perfusion in the coronary tree, and torso potential. Despite the robustness and accuracy of physics-based models, certain aspects, such as unveiling constitutive laws for cardiac cells and myocardial material properties, as well as devising efficient reduced order models to dominate the extraordinary computational complexity, have been successfully tackled by leveraging data-driven models. |
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