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 1356 products
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73/2026 - 09/28/2026
Corti, M.
A weighted polygonal discontinuous Galerkin method for hierarchically coupled reaction–diffusion systems with cubic interactions | Abstract | | We develop and analyse a symmetric weighted interior penalty polytopal discontinuous Galerkin (SWIP-PolyDG) method for multi-species reaction--diffusion systems with nonlinear reaction terms of up to cubic order. Such terms arise naturally when higher-order interactions are incorporated into population models, allowing non-additive effects among multiple species to influence local growth and conversion mechanisms. The proposed framework accommodates heterogeneous and possibly anisotropic diffusion tensors on general polygonal meshes. To control the nonlinear coupling, we consider a hierarchical block structure in the reaction operator, whereby each population block depends only on its own variables and on those associated with preceding blocks. In addition, the cubic self-interactions within each block are assumed to have a dissipative diagonal structure. Under these hypotheses and proceeding recursively over the hierarchy of population blocks, we derive local-in-time stability estimates in two spatial dimensions for the semi-discrete formulation in both the L2-and dG-norms. We further establish an a priori error estimate in a combined L2-dG energy norm for sufficiently regular solutions for the semi-discrete formulation. Finally, numerical experiments confirm the predicted convergence behaviour and illustrate the robustness of the method under heterogeneous diffusion. |
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72/2026 - 09/27/2026
Lorenzon, G.; Regazzoni, F.
Optimal Transport Dropout for Structured Predictive Uncertainty | Abstract | | Deterministic neural networks and neural operators provide point predictions with no intrinsic measure of reliability. Yet, predictive uncertainty may stem from irreducible outcome variability, finite data, or limitations of the chosen model class. Monte Carlo dropout offers a computationally convenient way to construct a predictive distribution through stochastic feature masking, without training multiple independent networks or explicitly inferring a posterior over model parameters. However, its perturbation law is largely prescribed a priori and typically factorised across latent coordinates. We introduce Optimal Transport Dropout (OTD), which instead learns the predictive mapping and the law of its latent perturbations jointly. Starting from a simple independent reference distribution, OTD transports latent perturbations through a learnable flow and propagates them through the predictive neural network, thereby inducing a structured predictive law. Training uses the strictly proper Energy Score, while a kinetic-action term geometrically regularises the transport. Synthetic benchmarks show that OTD captures multimodal predictive distributions, generates meaningful dispersion when the model is misspecified, and exhibits contracting dispersion as more training data or greater model capacity are provided. For a field-valued partial differential equation surrogate, predictive dispersion strongly aligns with the spatial pattern of prediction errors. On this task, compared with Monte Carlo dropout, OTD yields more accurate predictions and better-calibrated, substantially narrower intervals. On real-world regression benchmarks, it further shows competitive accuracy and better probabilistic predictions compared to several established baselines. OTD therefore offers a way to learn structured predictive uncertainty without explicit posterior inference or ensembles of independently trained predictors. |
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71/2026 - 09/24/2026
Radisic, I.; Regazzoni, F.; Dede', L.; Quarteroni, A.
A mathematical model for irreversible damage of the collagen scaffold in the myocardium | Abstract | | We propose a dissipative, irreversible damage model for anisotropic media in large deformations to address the damage process of the myocardium following a cardiac infarction. We model damage to the collagen in the cleavage planes resulting from an increased load to the passive tissue. Starting from variational principles, we derive a quasi-static differential model governing the irreversible evolution of the damage. We apply our model to two test cases. First, a rectangular passive slab geometry to which an indenter-like load is applied. Then, we couple our model with a model for the numerical simulation of left ventricular electromechanics. The computational results obtained with our novel mathematical model show that a redistribution of the load within a left ventricle occurring following a cardiac infarction can produce the damage to the collagen scaffold in the infarcted area consistent with experimental results. Our model and results support the evidence that passive load-dependent dissipative phenomena are implicated in post-infarction remodelling. |
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70/2026 - 09/24/2026
Micheletti, S.
Longitudinal versus quasi-P waves in weakly anisotropic elasticity: operator comparison and long-time dephasing | Abstract | | In isotropic elasticity, P-wave displacement is longitudinal and curl-free. In anisotropic elasticity, the physical quasi-P (qP) mode is instead selected by the principal eigenvector of the Christoffel matrix and is generally not parallel to the wave normal. We compare, in homogeneous two-dimensional vertical transverse isotropy (VTI), the exact elastic qP propagator with a longitudinally constrained propagator that suppresses transverse displacement by construction. Both dynamics are placed in a periodic operator and variational framework. The qP space is an invariant spectral subspace of the elastic operator, whereas the longitudinal space yields a Galerkin restriction that is generally not invariant. The corresponding forms are coercive on mean-zero $H^1$, their generators are positive self-adjoint operators of order two, and both Cauchy problems are well posed and energy conservative. A two-dimensional Rayleigh-quotient identity expresses the longitudinal squared-speed deficit as the qP--qSV spectral gap multiplied by the squared polarization mismatch. Building on classical weak-anisotropy perturbation theory, we derive an explicit VTI specialization of the qP projector and phase symbol. The projector error and qSV contamination are $O(eta)$ in amplitude, whereas the qP phase-speed error is $O(eta^2)$. For longitudinal initial data, the field error admits an orthogonal decomposition into modal contamination and qP dephasing. A uniform estimate bounds it by $C|eta||u_0|+Cteta^2|u_0|_{H^1}$ on bounded times. After removal of the common carrier, an abstract two-branch multiplier theorem gives field-level limits on the intermediate scale $t=tau/eta$ and the diffractive scale $t=tau/eta^2$. The first yields a finite polarization--phase crossover, whereas the second yields a generally order-one dephasing profile. Exact-in-time Fourier experiments verify the identities, asymptotic coefficients, convergence rates, and two long-time limits. The main contribution is therefore not a new local qP approximation, but a quantitative error theory describing when a longitudinal elastic model approximates the exact qP branch and when its second-order phase accuracy is exhausted by long-time dephasing. |
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69/2026 - 09/04/2026
Zecchi, A. A.; Ferro, N.; Perotto, S.
Complexity-controlled QUBO formulation for topology optimization via anisotropic mesh adaptation | Abstract | | QUBO formulation provides a natural route to address topology optimization of continuum structures with classical heuristic, quantum-inspired, and quantum annealing solvers. Their practical applicability, however, is still limited by the number of binary variables that can be handled, especially on near-term quantum hardware. In this work, we tackle this bottleneck by proposing QUBOSIMPATY algorithm which combines a QUBO formulation of the SIMP minimum compliance problem with anisotropic recovery-based mesh adaptation, enriched with metric-based complexity control.
Specifically, we exploit anisotropic mesh adaptation to reduce the number of density degrees of freedom, while retaining directional resolution along the sharp material-void interfaces that characterize optimized layouts. A metric rescaling procedure is applied to prescribe the number of mesh vertices, and hence the number of binary variables, so as to comply with the severe size constraints imposed by quantum annealing hardware.
Numerical tests in two and three dimensions are carried out with classical QUBO heuristics, including simulated annealing and tabu search. Moreover, a proof-of-concept experiment is performed on quantum annealing hardware. The results show that the proposed strategy improves the suppression of intermediate densities while keeping the optimization problem within the admissible size range. |
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68/2026 - 09/04/2026
Patanè, G.; Greven, S.; Menafoglio, A.
Random mixtures in Bayes Hilbert spaces | Abstract | | We present a framework for the analysis and unmixing of random density mixtures in the Bayes Hilbert space. General identifiability results for mixtures in Hilbert spaces are established and applied to the Bayes Hilbert space setting. Building on these results, we propose a penalised maximum likelihood approach for the unmixing of Bayes Hilbert mixtures aimed at recovering the statistically space-efficient representation, together with a computationally efficient coordinate-wise maximisation algorithm for its implementation. The methodology is illustrated through a hyperspectral data application, where observations can be naturally embedded in the Bayes Hilbert space and analyzed in terms of distributional shape rather than amplitude. A complementary simulation study demonstrates the interpretability and practical performance of the proposed approach. |
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67/2026 - 08/28/2026
Ciardulli, S.; Fontana, N.; Vantini, S.; Ieva F.
Generalized propensity score weighting for functional causal inference framework | Abstract | | Estimating causal effects in observational studies requires adjustment for confounding, a task that becomes challenging when the exposure is a function observed over a continuous domain rather than a scalar variable. We develop a functional propensity score weighting framework that achieves covariate balance by removing dependence between time-varying treatments and observed confounders, thereby enabling estimation of marginal causal effects in settings with functional treatments, covariates, and outcomes.
We propose a dual formulation of the weight estimation problem that yields a smooth unconstrained optimization and improves computational scalability. The proposed framework extends naturally to settings with time-varying covariates and to longitudinal outcomes via a function-on-function marginal structural model, allowing estimation of causal effect surfaces. The proposed method improves covariate balance, estimation accuracy, and computational efficiency compared to the existing approach and retains these properties when extended to functional covariates and outcomes. We apply the method to data from the UK Biobank to estimate the causal effect of body mass index trajectories on the risk of Type 2 Diabetes and on subsequent glycated hemoglobin trajectories, a functional measure of metabolic status. |
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66/2026 - 07/28/2026
Antonietti, P.F.;Bonizzoni, F.;Corti, M.; De March, N.;Di Noto, S.;Regazzoni, F.
A stability-preserving polytopal discontinuous Galerkin method for the Fisher-Kolmogorov model with applications to neurodegenerative diseases | Abstract | | The Fisher-Kolmogorov model is one of the most widely used models in the study of neurodegenerative diseases, owing to its simple structure as a nonlinear reaction-diffusion equation. In particular, it is commonly employed to describe proteinopathies such as Alzheimer's and Parkinson's diseases. Under suitable assumptions, non-negativity of the solution is guaranteed at the continuous level, which is physically relevant since the solution represents a relative concentration. However, this property is not generally preserved at the discrete level, potentially leading to unphysical and unstable numerical approximations.
In this work, we analyze a modified version of the Fisher-Kolmogorov model that stabilizes the dynamics around the unstable equilibrium c=0. For the spatial discretization, we adopt a discontinuous Galerkin method on polygonal and polyhedral meshes, coupled with the Crank--Nicolson scheme for time integration. We derive stability and a-priori error estimates for the semi-discrete problem.
The theoretical findings are supported by numerical experiments, including convergence studies in both two and three dimensions. Finally, we validate the model through simulations of alpha-synuclein diffusion in a two-dimensional agglomerated brain section, demonstrating the high-order accuracy and robustness of the proposed method. |
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