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 1320 products
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35/2026 - 04/20/2026
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 - 04/14/2026
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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33/2026 - 04/12/2026
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. |
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32/2026 - 04/09/2026
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. |
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31/2026 - 04/04/2026
Guastamacchia, C.; Piersanti, R; Giardini, F.; Coppini, R.; Ferrantini C.; Dede’ L.; Sacconi L.; Regazzoni F.
The functional impact of myofiber macroscopic organization and disarray in computational models of the murine heart | Abstract | | A major challenge in computational models of cardiac electromechanics is the reconstruction of myocardial fiber architecture, as direct in vivo measurements of fiber orientation are not feasible. Consequently, rule-based methods are commonly adopted as surrogates, relying on empirical descriptions of fiber organization combined with patient-specific geometries. This study investigates the respective roles of macroscopic fiber architecture and microscopic fiber disarray in cardiac electromechanical simulations. A high-fidelity biventricular electromechanical model of a murine heart was developed using a high-resolution myocardial
fiber field obtained via mesoscopic optical imaging, which serves as a reference ground truth. A spatial smoothing strategy is introduced to decouple macroscopic fiber organization from local disarray, and the resulting responses are also compared with those obtained using a rule-based fiber field. The results show that passive mechanics and electrophysiological activation are only weakly affected by fiber disarray, with global chamber compliance and activation times remaining largely unchanged across different fiber descriptions. In contrast, active mechanics is highly sensitive to fiber architecture. Moderate regularization of the
experimentally measured fiber field enhances the ventricular pumping efficiency of the computational model by reducing microscopic disarray while preserving the macroscopic helical organization, whereas excessive smoothing or rule-based fiber reconstructions lead to unphysiologically strong or inefficient contraction.
Within this framework, two commonly adopted surrogate strategies to account for fiber disarray are investigated: (i) a reduction of the effective cross-bridge stiffness in the active tension model, and (ii) the introduction of controlled misalignment between active tension and the local fiber direction. While both approaches reproduce global hemodynamic indicators comparable to the reference case, an effective reduction of contractility – despite its phenomenological nature – provides a closer match to the reference strain patterns than the introduction of orthogonal active stress components. Overall, the results highlight the dominant role of macroscopic fiber architecture in active mechanics and reveal important limitations of commonly adopted surrogate approaches for modeling fiber disarray. |
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30/2026 - 03/31/2026
Regazzoni, F.
The internal law of a material can be discovered from its boundary | Abstract | | Since the earliest stages of human civilization, advances in technology have been tightly linked to our ability to understand and predict the mechanical behavior of materials. In recent years, this challenge has increasingly been framed within the broader paradigm of data-driven scientific discovery, where governing laws are inferred directly from observations. However, existing methods require either stress-strain pairs or full-field displacement measurements, which are often inaccessible in practice. We introduce Neural-DFEM, a method that enables unsupervised discovery of hyperelastic material laws even from partial observations, such as boundary-only measurements. The method embeds a differentiable finite element solver within the learning loop, directly linking candidate energy functionals to available measurements. To guarantee thermodynamic consistency and mathematical well-posedness throughout training, the method employs Hyperelastic Neural Networks, a novel structure-preserving neural architecture that enforces frame indifference, material symmetry, polyconvexity, and coercivity by design. The resulting framework enables robust material model discovery in both two- and three-dimensional settings, including scenarios with boundary-only measurements. Neural-DFEM allows for generalization across geometries and loading conditions, and exhibits unprecedented accuracy and strong resilience to measurement noise. Our results demonstrate that reliable identification of material laws is achievable even under partial observability when strong physical inductive biases are embedded in the learning architecture. |
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28/2026 - 03/19/2026
Daniele, F.; Leimer Saglio, C. B.; Pagani, S.; Antonietti, P. F.
Mathematical and numerical modeling of coupled oxygen dynamics and neuronal electrophysiology | Abstract | | Modeling and simulating how oxygen supply shapes neuronal excitability is crucial for advancing the understanding of brain function in pathological scenarios, such as ischemia. This condition is caused by a reduced blood supply, leading to the deprivation of oxygen and other metabolites; this energy deficit impairs ionic pumps and causes cellular swelling. In this work, this phenomenon is modeled through a volumetric variation law that links cell swelling to local oxygen concentration and the percentage of blood flow reduction. The swelling law links volume changes to local oxygen and the degree of blood-flow depression, providing a simple mechanistic pathway from hypoxia to tortuosity-driven transport impairment. The interplay between oxygen supply and excitability in brain tissue is described by coupling the monodomain model with specific neuronal ionic and metabolic models that characterize ion and metabolite concentration dynamics.
The numerical approximation of this coupled multiscale problem is particularly challenging, owing to the presence of sharp and fast-propagating wavefronts and complex geometrical domains.
To address these challenges, suitable space- and time-adaptive schemes are employed to capture the action potential dynamics accurately.
This multiscale model is discretized in space with the high-order p-adaptive discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and integrated in time with a Crank-Nicolson scheme. We numerically investigate different pathological scenarios on a two-dimensional idealized square domain and on a realistic geometry, both discretized with a polygonal grid, analyzing how subclinical and severe ischemia can affect brain electrophysiology and metabolic concentrations. |
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27/2026 - 03/09/2026
Antonietti, P. F.; Abdalla, O. M. O.; Garroni, M. G.; Mazzieri, I.; Parolini, N.
A hybrid reduced-order and high-fidelity discontinuous Galerkin Spectral Element framework for large-scale PMUT array simulations | Abstract | | Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) are essential for next-generation ultrasonic sensing and imaging due to their bidirectional electromechanical behavior, compact design, and compatibility with low-voltage electronics. As PMUT arrays grow in size and complexity, efficiently modeling their coupled electromechanical-acoustic behavior becomes increasingly challenging. This work presents a novel computational framework that combines model order reduction with a Discontinuous Galerkin Spectral Element Method (DGSEM) paradigm to simulate large PMUT arrays. Each PMUT’s mechanical behavior is represented using a reduced set of vibration modes, which are coupled to an acoustic domain model to describe the full array. To further improve efficiency, a secondary acoustic domain is connected via DG interfaces, enabling non-conforming mesh refinement, with variable approximation order, and accurate wave propagation. The framework is implemented
in the SPectral Elements in Elastodynamics with Discontinuous Galerkin (SPEED) software, an open-source, parallelized platform leveraging domain decomposition, high-order polynomials, METIS graph partitioning, and MPI for scalable performance. The proposed methodology addresses key challenges in meshing, supporting high-fidelity simulations for both PMUT transmission and reception phases. Numerical results demonstrate the framework’s accuracy, scalability, and efficiency for large PMUT array simulations. |
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