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 1326 prodotti
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40/2026 - 28/05/2026
Marchesin, L.; Menafoglio, A.; Secchi, P.
A Convolution Process for Sea Surface Temperature Hot-Spot Identification in the Mediterranean Sea | Abstract | | Sea surface temperature (SST) is a fundamental determinant of global climate dynamics and economic activity. Reliable projections of future SST patterns depend critically on a rigorous characterization of the underlying spatial random field. In this study, we introduce a novel convolution-based covariance framework tailored to geostatistical domains constrained by physical barriers and influenced by vector-driven flows. By discretizing the continuous marine domain into a directed linear network that preserves the orientation of ocean currents, we construct a moving-average stochastic process whose dynamic is encoded via a Markovian transitionprobability matrix on the network’s vertices. The induced covariance structure emerges as a weighted combination of a spatial kernel and flow-dependent weights, giving rise to a complex
estimation problem. To stabilize inference, we propose a penalized estimator that regularizes covariance parameters while enforcing consistency with known hydrodynamic properties. We then embed this covariance model into a Monte Carlo simulation framework to refine RCPbased SST projections and to identify thermal “hot spots” of heightened ecological risk. Our approach delivers a statistically principled framework that prevents physical inconsistencies –
such as correlations across land barriers – providing a robust basis for quantifying uncertainty in future SST forecasts and for guiding targeted environmental assessments. |
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41/2026 - 28/05/2026
Sosta, L.; Ciancarelli, C; Marini, L.; Pagani, S.; Regazzoni, F.; Parolini, N.
Physics-constrained identification of graph-based thermal networks for spacecraft digital twins | Abstract | | Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To address this,
we introduce a physically-constrained calibration framework for Lumped Parameter Thermal Models (LPTMs), formulated as a trajectory-based inverse problem for graph dynamical systems. The model reconstructs thermal dynamics directly from temperature measurements and known inputs, without relying on a priori parameter values derived from material properties or geometric assumptions.
Physical admissibility is enforced at the parameterization level: positivity of nodal coefficients and symmetry of conductive interactions are imposed by construction. This guarantees stable dynamics and restricts the identification problem to a physically meaningful parameter space, improving conditioning without the need of additional regularization.
The identification problem is addressed through trajectory matching, ensuring stable rollout over extended time horizons.
The methodology is validated on synthetic datasets generated from high-fidelity finite element simulations under progressively complex forcing conditions. The calibrated LPTMs accurately reproduce long-term temperature evolution and exhibit robustness to measurement noise.
The proposed framework provides a systematic approach to the calibration of reduced-order thermal models by combining physical structure with data-driven identification. The numerical results show a favorable balance between accuracy and computational efficiency, making the models suitable for integration in spacecraft thermal Digital Twin applications. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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