Quaderni MOX
Pubblicazioni
del Laboratorio di Modellistica e Calcolo Scientifico MOX. I lavori riguardano prevalentemente il campo dell'analisi numerica, della statistica e della modellistica matematica applicata a problemi di interesse ingegneristico. Il sito del Laboratorio MOX è raggiungibile
all'indirizzo mox.polimi.it
Trovati 1324 prodotti
-
38/2026 - 14/05/2026
Clemente, A.; Arnone, E.; Mateu, J.; Sangalli, L.M.
Nonparametric estimators over metric graphs | Abstract | | This work discusses a theory of functional spaces over metric graphs, that permits the definition of penalized likelihood methods for data observed over spatial supports that are graphs. Within the considered mathematical framework, we recover classical results in functional analysis, such as a Poincaré-type inequality. This, in turn, enables us to uplift, to the considered setting, the theory of some fundamental penalized likelihood methods. Specifically, we present two important classes of statistical models: nonparametric regression and nonparametric density estimation, here defined for data observed over graphs. We derive theoretical results regarding the well-posedness of the associated estimation problems and the consistency of the estimators. We also demonstrate the performances of the defined estimators with respect to state-of-art alternatives. |
-
39/2026 - 14/05/2026
Patanè, G.; Menafoglio, A.; Krauth, A.; Fechner, P.; Dede', L.; Colosimo, B.M.; Nicolussi, F.
K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles | Abstract | | Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure. |
-
37/2026 - 07/05/2026
Centofanti, E.; Ziarelli, G.; Scacchi, S.; Pavarino, L.F.
A Neural Latent Dynamics Approach for Solving Inverse Problems in Cardiac Electrophysiology | Abstract | | Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness and the prohibitive computational complexity of PDE-constrained optimization. In this work, we introduce
a data-driven framework leveraging Latent Dynamics Networks (LDNets) to construct efficient surrogate models of the forward operator. By mapping low-dimensional parameters, representing ectopic activation sites or ischemic region descriptors, to the ECG signals via latent dynamics governed by neural ordinary differential equations, our approach circumvents the computational burden of evaluating high-fidelity cardiac models during iterative parameter estimation. The surrogate is trained offline on high-fidelity data, enabling rapid and robust inversion. We validate the proposed framework through rigorous numerical experiments with synthetic data across both 2d and 3d geometries. Results show that the LDNet-based surrogate achieves precise reconstruction of cardiac parameters while drastically reducing computational overhead, thereby enabling near real-time clinical applications. |
-
36/2026 - 05/05/2026
Botti, M.; Mascotto, L.; Mosconi, M.
A nonconforming method for a generalized Darcy-Forchheimer model | Abstract | | We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed in [V. Girault and M. F. Wheeler. Numerical discretization of a Darcy-Forchheimer model. Numer. Math. 2008], we consider general, i.e., non-quadratic, Forchheimer nonlinearities; we admit mixed, inhomogeneous boundary conditions; we allow for more general, i.e., with lower Lebesgue regularity, permeability tensors; we construct general-order schemes; we prove convergence to the exact solution under low regularity assumptions, based on novel Sobolev-trace inequalities for broken spaces; we derive error estimates of general-order assuming extra regularity of the exact solution and data; we present numerical results assessing the performance of the proposed schemes for different types of nonlinearity and nonlinear solvers. |
-
35/2026 - 20/04/2026
Caon, B.; Corti, M.; Bonizzoni, F.; Antonietti, P.F.
High-fidelity and Network-based Spatio-temporal Mathematical Models of Alzheimer's Disease Progression and their Validation Against PET-SUVR Imaging Data | Abstract | | Alzheimer's disease is the most common neurodegenerative disorder. Its pathological development is connected with the misfolding and accumulation of two toxic proteins: amyloid-beta and tau proteins. Mathematical models provide a valuable quantitative tool for monitoring disease progression. In this work, we proposed and compare a novel framework where the spatio-temporal dynamics of amyloid-beta and tau proteins is modeled based on employing either three-dimensional patient-specific geometries or through reduced network-based models defined on the brain connectome. More specifically, a high-fidelity biophysical model is proposed on three-dimensional brain geometries reconstructed from magnetic resonance imaging, whereas a network-based reduced formulation is defined on the brain connectome. For both approaches, a suitable numerical discretisation is proposed. A sensitivity analysis is presented to quantify the influence of model parameters on protein concentration patterns as well as compare the quality of the predictions. For both approaches, the results are validated against PET-SUVR clinical data using [18F]AZD4694 for amyloid-beta and [18F]MK6240 for tau protein. The results indicate that the three-dimensional model provides the most accurate and biologically consistent description of the disease progression, but remains computationally demanding. On the other hand, the reduced graph-based model is cheaper, but it is not always able to achieve reliable results. |
-
34/2026 - 14/04/2026
Mancinelli, F. M.; Torzoni, M.; Maisto, D.; Donnarumma, F.; Corigliano, A.; Pezzulo, G.; Manzoni, A.
Multi-Agent Digital Twins for strategic decision-making using Active Inference | Abstract | | Active Inference is an emerging framework providing a quantitative account of behavioral processes in neuroscience and a principled approach to decision-making under uncertainty. Its application to agency problems is natural, offering an autopoietic interpretation of action while addressing classical challenges such as the exploration-exploitation trade-off. Recently, Active Inference has been applied to digital twin scenarios for adaptive and predictive modeling of complex systems. In this work, we extend Active Inference to multi-agent digital twins in which agents interact within a shared environment while maintaining decentralized generative models. Our multi-agent framework features two innovations: (i) contextual inference to improve adaptability in dynamic environments, and (ii) the integration of streaming machine learning within agents' generative structures, enabling tunable goal-oriented behavior while preserving efficiency and scalability. The framework is illustrated through a Cournot competition example, providing a digital twin representation of a socio-economic system and highlighting its potential for coordinated decision-making in multi-agent contexts. |
-
33/2026 - 12/04/2026
Franzoni, G.; Mirabella, S.; Dabek, A.; Ferro, N.; Antona, A.; Carlessi, M.; Cinquemani, S.; Matteucci, M.; Cocetta, G.; Perotto, S.
Integrating Environmental Control and Hyperspectral Imaging to Assess Light and Nutrient Effects on Lettuce Post-Harvest Quality in Vertical Farming | Abstract | | Vertical farming offers an opportunity to optimize crop yield and quality through precise control of environmental factors. In this study, we investigated the effects of light spectrum composition and nutrient solution electrical conductivity (EC) on yield and on biochemical traits of lettuce (Lactuca sativa L. cv. Lollo Rosso) grown in a vertical farm. The experimental design combined three light treatments (high blue, low blue, and variable blue ratio) with three nutrient solution EC levels (1, 2, and 3 dS/m), resulting in nine treatment conditions. Plants were harvested twice, and destructive analyses were conducted at harvest time and after 14 days of cold storage to assess yield, water content, pigments, sugars, nitrates, anthocyanins, phenolics, and electrolyte leakage. Results showed that lettuce growth and quality were influenced by both nutrient solution composition and light spectrum: higher salt concentration enhanced growth but not yield, while blue light promoted plant compactness. Diluted solutions increased secondary metabolites under mild nutrient stress, with limited effects on pigment content, sugar dynamics, and postharvest preservation. As a complementary analysis, hyperspectral imaging (400–1000 nm) was applied to lettuce leaves. Spectral data were analysed using machine learning models to investigate the relationship between changes in reflectance and in chemical composition, by comparing leaves at harvest with those after 14 days of cold storage. The adopted approach demonstrated the feasibility of using hyperspectral imaging to classify lettuce leaves
at different post-harvest stages and identified candidate combinations of spectral indices capable of capturing the degradation of specific chemical traits occurring during the storage period. Overall, this study highlights the central role of nutrient solution concentration and light spectrum in determining lettuce yield and quality in vertical farming, while demonstrating the added value of hyperspectral imaging as a supplementary approach for trait assessment. |
-
32/2026 - 09/04/2026
Antonietti, P.F.; Bonizzoni, F.; Perugia, I.; Verani, M.
A Multilevel Monte Carlo Virtual Element Method for Uncertainty Quantification of Elliptic Partial Differential Equations | Abstract | | We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for
the statistical approximation error for both the solution and suitable linear quantities of interest. A Multilevel Monte Carlo Virtual Element method is also developed and analyzed to mitigate the computational
cost of the plain Monte Carlo strategy. The proposed approach exploits the flexibility of the Virtual Element method on general polytopal meshes and employs sequences of coarser spaces constructed via mesh agglomeration, providing a practical realization of the multilevel hierarchy even in complex geometries. This strategy substantially reduces the number of samples required on the finest level to achieve a prescribed accuracy. We prove convergence of the multilevel method and analyze its computational complexity, showing that it yields
significant cost reductions compared to standard Monte Carlo methods for a prescribed accuracy. Extensive numerical experiments support the theoretical results and demonstrate the efficiency of the proposed method. |
|
