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 1326 products
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25/2026 - 03/04/2026
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 - 02/27/2026
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 - 02/23/2026
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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19/2026 - 02/23/2026
Caldera, L.; Cavinato, L.; Ieva, F.
Scanner-agnostic MRI harmonization via SSIM-guided disentaglement | Abstract | | The variability introduced by differences in MRI scanner models, acquisition protocols, and imaging sites hinders consistent analysis and generalizability across multicenter studies. We present a novel image-based harmonization framework for 3D T1-weighted brain MRI, which disentangles anatomical content from scanner- and site-specific variations. The model incorporates a differentiable loss based on the Structural Similarity Index (SSIM) to preserve biologically meaningful features while reducing inter-site variability. This loss enables separate evaluation of image luminance, contrast, and structural components. Training and validation were performed on multiple publicly available datasets spanning diverse scanners and sites, with testing on both healthy and clinical populations. Harmonization using multiple style targets, including style-agnostic references, produced consistent and high-quality outputs. Visual comparisons, voxel intensity distributions, and SSIM-based metrics demonstrated that harmonized images achieved strong alignment across acquisition settings while maintaining anatomical fidelity. Following harmonization, structural SSIM reached 0.97, luminance SSIM ranged from 0.98 to 0.99, and Wasserstein distances between mean voxel intensity distributions decreased substantially. Downstream tasks showed substantial improvements: mean absolute error for brain age prediction decreased from 5.36 to 3.30 years, and Alzheimer’s disease classification AUC increased from 0.78 to 0.85. Overall, our framework enhances cross-site image consistency, preserves anatomical fidelity, and improves downstream model performance, providing a robust and generalizable solution for large-scale multicenter neuroimaging studies. |
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17/2026 - 02/23/2026
Caldera, L.; Bottacini, G.; Cavinato, L.
MAGIC-Flow: multiscale adaptive conditional flows for generation and interpretable classification | Abstract | | Generative modeling has emerged as a powerful paradigm for representation learning, but its direct applicability to challenging fields like medical imaging remains limited: mere generation, without task alignment, fails to provide a robust foundation for clinical use. We propose MAGIC-Flow, a conditional multiscale normalizing flow architecture that performs generation and classification within a single modular framework. The model is built as a hierarchy of invertible and differentiable bijections, where the Jacobian determinant factorizes across sub-transformations. We show how this ensures exact likelihood computation and stable optimization, while invertibility enables explicit visualization of sample likelihoods, providing an interpretable lens into the model’s reasoning. By conditioning on class labels, MAGIC-Flow supports controllable sample synthesis and principled class-probability estimation, effectively aiding both generative and discriminative objectives. We evaluate MAGIC-Flow against top baselines using metrics for similarity, fidelity, and diversity. Across multiple datasets, it addresses generation and classification under scanner noise, and modality-specific synthesis and identification. Results show MAGIC-Flow creates realistic, diverse samples and improves classification. MAGIC-Flow is an effective strategy for generation and classification in data-limited domains, with direct benefits for privacy-preserving augmentation, robust generalization, and trustworthy medical AI. |
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15/2026 - 02/16/2026
Zecchi, A. A.; Sanavio, C.; Cappelli, L.; Perotto, S.; Roggero, A.; Succi, S.
Block encoding of sparse matrices with a periodic diagonal structure | Abstract | | Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is based on the linear combination of unitaries (LCU) framework and on an efficient unitary operator used to project the complex exponential at a frequency $omega$ multiplied by the computational basis into its real and imaginary components.
We demonstrate a distinct computational advantage with a $mathcal{O}(text{poly}(n))$ gate complexity, where $n$ is the number of qubits, in the worst-case scenario used for banded matrices, and $mathcal{O}(n)$ when dealing with a simple diagonal matrix, compared to the exponential scaling of general-purpose methods for dense matrices. Various applications for the presented methodology are discussed in the context of solving differential problems such as the advection-diffusion-reaction (ADR) dynamics, using quantum algorithms with optimal scaling, e.g., quantum singular value transformation (QSVT). Numerical results are used to validate the analytical formulation. |
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14/2026 - 02/09/2026
Agasisti, T.; Cannistrà, M.; Paganoni, A.M.
Nudging communication for students at risk: experimental evidence from an Italian university | Abstract | | To address the dropout issue in an Italian university, this research deals with stimulating at-risk students to enroll in tutoring services. Students with a predicted dropout risk are assigned to different nudging communication treatments via email through a rigorous randomized controlled trial. Findings highlight that messages based on a “social comparison” nudge obtains positive and statistically significant effects to increase students’ propensity towards attending tutoring services. |
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13/2026 - 02/05/2026
Dimola, N.; Coclite, A.; Zunino, P.
Neural Preconditioning via Krylov Subspace Geometry | Abstract | | We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). Such systems are typically ill-conditioned due to embedded lower-dimensional structures and are solved using Krylov subspace methods. Our approach yields an approximation of the inverse operator employing a learning algorithm consisting of a two-stage training framework: an initial static pretraining phase, based on residual minimization, followed by a dynamic fine-tuning phase that incorporates solver convergence dynamics into the training process via a novel loss functional. This dynamic loss is defined by the principal angles between the residuals and the Krylov subspaces. It is evaluated using a differentiable implementation of the Flexible GMRES algorithm, which enables backpropagation through both the Arnoldi process and Givens rotations. The resulting neural preconditioner is explicitly optimized to enhance early-stage convergence and reduce iteration counts across a family of 3D–1D mixed-dimensional problems exhibiting geometric variability in the 1D domain. Numerical experiments show that our solver-aligned approach significantly improves convergence rate, robustness, and generalization.
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