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 1315 prodotti
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30/2026 - 31/03/2026
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 - 19/03/2026
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 - 09/03/2026
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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23/2026 - 04/03/2026
Ballini, E.; Muscarnera, L.; Fumagalli, A.; Scotti, A.; Regazzoni, F.
Elimination-compensation pruning for fully-connected neural networks | Abstract | | The unmatched ability of deep neural networks to capture complex patterns in large and noisy datasets is often associated with their large hypothesis space and the vast number of parameters characterizing modern architectures. Pruning techniques have emerged as effective tools to extract sparse representations of neural network parameters while preserving accuracy. However, a fundamental assumption behind pruning is that expendable weights have a small impact on the network error, whereas highly important weights exert a larger influence on inference.
We argue that this idea could be generalized; what if a weight is not simply removed but also compensated with a perturbation of the adjacent bias, which does not contribute to the network sparsity? Our work introduces a novel pruning method in which the importance measure of each weight is computed considering the output behavior after an optimal perturbation of its adjacent bias.
These perturbations can be then applied directly after the removal of each weight, independently of each other. After deriving analytical expressions for the aforementioned quantities, numerical experiments are conducted to benchmark this technique against some of the most popular pruning strategies, demonstrating an intrinsic efficiency of the proposed approach in very diverse machine learning scenarios. |
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26/2026 - 04/03/2026
Dokuchaev, A.; Bonizzoni, F.; Pagani, S.; Regazzoni, F.; Pezzuto, S.
Learning geometry-dependent lead-field operators for forward ECG modeling | Abstract | | Modern forward electrocardiogram (ECG) computational models rely on an accurate representation of the torso domain. The lead-field method enables fast ECG simulations while preserving full geometric fidelity. Achieving high anatomical accuracy in torso representation is, however, challenging in clinical practice, as imaging protocols are typically focused on the heart and often do not include the entire torso. In addition, the computational cost of the lead-field method scales linearly with the number of electrodes, limiting its applicability in high-density recording settings. To date, no existing approach simultaneously achieves high anatomical fidelity, low data requirements and computational efficiency. In this work, we propose a shape-informed surrogate model of the lead-field operator that serves as a drop-in replacement for the full-order model in forward ECG simulations. The proposed framework consists of two components: a geometry-encoding module that maps anatomical shapes into a low-dimensional latent space, and a geometry-conditioned neural surrogate that predicts lead-field gradients from spatial coordinates, electrode positions and latent codes. The proposed method achieves high accuracy in approximating lead fields both within the torso (mean angular error <5°) and inside the heart, resulting in highly accurate ECG simulations (relative mean squared error <2.5%). The surrogate consistently outperforms the widely used pseudo lead-field approximation while preserving negligible inference cost. Owing to its compact latent representation, the method does not require a fully detailed torso segmentation and can therefore be deployed in data-limited settings while preserving high-fidelity ECG simulations. |
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25/2026 - 04/03/2026
Carrara, D.; Hirschvogel, M.; Bonizzoni, F.; Pagani, S.; Pezzuto, S.; Regazzoni, F.
Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation | Abstract | | High-fidelity computational models of cardiac mechanics provide mechanistic insight into the heart function but are computationally prohibitive for routine clinical use. Surrogate models can accelerate simulations, but generalization across diverse anatomies is challenging, particularly in data-scarce settings. We propose a two-step framework that decouples geometric representation from learning the physics response, to enable shape-informed surrogate modeling under data-scarce conditions. First, a shape model learns a compact latent representation of left ventricular geometries. The learned latent space effectively encodes anatomies and enables synthetic geometries generation for data augmentation. Second, a neural field-based surrogate model, conditioned on this geometric encoding, is trained to predict ventricular displacement under external loading. The proposed architecture performs positional encoding by using universal ventricular coordinates, which improves generalization across diverse anatomies. Geometric variability is encoded using two alternative strategies, which are systematically compared: a PCA-based approach suitable for working with point cloud representations of geometries, and a DeepSDF-based implicit neural representation learned directly from point clouds. Overall, our results, obtained on idealized and patient-specific datasets, show that the proposed approaches allow for accurate predictions and generalization to unseen geometries, and robustness to noisy or sparsely sampled inputs. |
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21/2026 - 27/02/2026
Bottacini, G.; Torzoni, M.; Manzoni, A.
Neural Markov chain Monte Carlo: Bayesian inversion via normalizing flows and variational autoencoders | Abstract | | This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that must be solved multiple times and are characterized by intractable or unavailable likelihood functions. The posterior probability distribution over quantities of interest is estimated via differential evolution Metropolis sampling, empowered by learnable mappings. First, a variational autoencoder performs probabilistic feature extraction from observational data. The resulting latent structure inherently quantifies uncertainty, capturing deviations between the actual data-generating process and the training data distribution. At each step of the MCMC random walk, the algorithm jointly samples from the data-informed latent distribution and the space of parameters to be inferred. These samples are fed into a neural likelihood estimator based on normalizing flows, specifically real-valued non-volume preserving transformations. The scaling and translation functions of the affine coupling layers are modeled by neural networks conditioned on the unknown parameters, allowing the representation of arbitrary observation likelihoods. The proposed methodology is validated on two case studies: structural health monitoring of a railway bridge for damage detection, localization, and quantification, and estimation of the conductivity field in a steady-state Darcy’s groundwater flow problem. The results demonstrate the efficiency of the inference strategy, while ensuring that model-reality mismatches do not yield overconfident, yet inaccurate, estimates. |
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20/2026 - 23/02/2026
Caldera, L.; Cavinato, L.; Cirone, A.; Cama, I.; Garbarino, S.; Lodi, R.; Tagliavini, F.; Nigri, A.; De Francesco, S.; Cappozzo, A.; Piana, M.; Ieva, F.;
DISARM++: Beyond scanner-free harmonization | Abstract | | Harmonization of T1-weighted MR images across different scanners is crucial for ensuring consistency in neuroimaging studies. This study introduces a novel approach to direct image harmonization, moving beyond feature standardization to ensure that extracted features remain inherently reliable for downstream analysis. Our method enables image transfer in two ways: (1) mapping images to a scanner-free space for uniform appearance across all scanners, and (2) transforming images into the domain of a specific scanner used in model training, embedding its unique characteristics. Our approach presents strong generalization capability, even for unseen scanners not included in the training phase. We validated our method using MR images from diverse cohorts, including healthy controls, traveling subjects, and individuals with Alzheimer’s disease (AD). The model’s effectiveness is tested in multiple applications, such as brain age prediction (R2 = 0.60 pm 0.05), biomarker extraction, AD classification (Test Accuracy = 0.86 pm 0.03), and diagnosis prediction (AUC = 0.95). In all cases, our harmonization technique outperforms state-of-the-art methods, showing improvements in both reliability and predictive accuracy. Moreover, our approach eliminates the need for extensive preprocessing steps, such as skull-stripping, which can introduce errors by misclassifying brain and non-brain structures. This makes our method particularly suitable for applications that require full-head analysis, including research on head trauma and cranial deformities. Additionally, our harmonization model does not require retraining for new datasets, allowing smooth integration into various neuroimaging workflows. By ensuring scanner-invariant image quality, our approach provides a robust and efficient solution for improving neuroimaging studies across diverse settings. |
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