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 1349 products
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66/2026 - 07/28/2026
Antonietti, P.F.;Bonizzoni, F.;Corti, M.; De March, N.;Di Noto, S.;Regazzoni, F.
A stability-preserving polytopal discontinuous Galerkin method for the Fisher-Kolmogorov model with applications to neurodegenerative diseases | Abstract | | The Fisher-Kolmogorov model is one of the most widely used models in the study of neurodegenerative diseases, owing to its simple structure as a nonlinear reaction-diffusion equation. In particular, it is commonly employed to describe proteinopathies such as Alzheimer's and Parkinson's diseases. Under suitable assumptions, non-negativity of the solution is guaranteed at the continuous level, which is physically relevant since the solution represents a relative concentration. However, this property is not generally preserved at the discrete level, potentially leading to unphysical and unstable numerical approximations.
In this work, we analyze a modified version of the Fisher-Kolmogorov model that stabilizes the dynamics around the unstable equilibrium c=0. For the spatial discretization, we adopt a discontinuous Galerkin method on polygonal and polyhedral meshes, coupled with the Crank--Nicolson scheme for time integration. We derive stability and a-priori error estimates for the semi-discrete problem.
The theoretical findings are supported by numerical experiments, including convergence studies in both two and three dimensions. Finally, we validate the model through simulations of alpha-synuclein diffusion in a two-dimensional agglomerated brain section, demonstrating the high-order accuracy and robustness of the proposed method. |
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65/2026 - 07/17/2026
De Sanctis, M.F.; Arnone, E.; Ieva, F.; Sangalli, L.M.
Modeling group heterogeneity in spatio-temporal data via physics-informed regression | Abstract | | We propose a physics-informed semiparametric framework for modeling spatiotemporal data with group structure. The approach extends classical mixed effects regression by incorporating a nonparametric space–time component, regularized through a partial differential equation to encode the underlying physical dynamics, while random effects capture group-specific variability. Estimation is carried out via a two-step procedure based on a functional extension of the Iteratively Reweighted Least Squares algorithm. We establish asymptotic properties of both fixed and random effect estimators and we assess the performance of the method through simulation studies against state-of-the-art alternatives. The proposed framework is applied to hourly nitrogen dioxide data over Lombardy (Italy), where random effects account for measurement heterogeneity across monitoring stations with different sensor technologies, demonstrating its effectiveness in capturing both physical dynamics and group heterogeneity. |
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64/2026 - 07/15/2026
Radisic, I.; Tirotta, R.; Zingaro, A.; Pagani, S.; Dede', L.
Physics-Informed Neural Networks for the High-Resolution Reconstruction of Flow Measurement Indicators in Fluid Dynamics | Abstract | | Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier-Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators. |
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63/2026 - 07/01/2026
Ciaramella, G.; Gong, W.; Kwok, F., Tan, Z.
Uniform Convergence of the Schwarz Alternating Method for Optimal Control Problems | Abstract | | In this paper, we analyze the Schwarz alternating method for unconstrained elliptic optimal control problems, which is equivalent to the corresponding method for the associated saddle-point systems. A distinctive feature in this setting is that the local error propagation operators are not necessarily nonexpansive in the energy norm, which stands in marked contrast to the standard elliptic boundary-value case. We develop a rigorous uniform convergence theory in the continuous setting and then extend the analysis to finite difference discretizations. In both formulations, we prove that the Schwarz iteration converges whenever its counterpart for the underlying elliptic equation is convergent. Furthermore, we show that the contraction factor for the auxiliary elliptic equation in the maximum norm provides a uniform upper bound, which is independent of the regularization parameter $alpha$, for the contraction factor of the optimal control iteration in the same norm. The theoretical framework is also extended to cover one-level alternating Schwarz and parallel Schwarz variants. Numerical experiments are presented to validate the theoretical results. |
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62/2026 - 07/01/2026
Ciaramella, G.; Gong, W.; Kwok, F.; Tan, Z.
On the Uniform Convergence Analysis of the Schwarz Alternating Method for Optimal Control Problems | Abstract | | In this paper, we investigate the uniform convergence of the Schwarz alternating method for unconstrained elliptic optimal control problems in one dimension. We derive the convergence factor of the method and find that the convergence factor of the method can be uniformly bounded by a factor ($<1$) associated with that for the state equation. We also observe that the local error propagation operators of the method under a standard choice of energy norms in the robust analysis of optimal control problems are nonexpansive. These observations indicate that the existing convergence analysis frameworks of domain decomposition methods for PDEs based on the standard choice of energy norms are not straightforwardly applicable to that for optimal control problems. |
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60/2026 - 07/01/2026
Ciaramella, G.; Gander, M.J.; Van Criekingen, S.; Vanzan, T.
Algebraic and Two-Level Parallel Substructured Schwarz Methods | Abstract | | Substructured Schwarz methods are interpretations of classical volume Schwarz methods as algorithms on interface variables. We introduce here a new parallel algebraic trace characterization to supersede the
geometric identification of the substructure within our petscs-based implementation of the parallel Schwarz method (equivalent to RAS).
We moreover consider a two-level substructured method with coarse space functions defined exclusively on the skeleton, and propose an additive version of the two-level preconditioner which significantly decreases the computing time. Weak scaling numerical results up to several thousands of CPU cores (one per subdomain) are presented
for the one- and two-level methods, comparing substructured and classical volume methods. |
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58/2026 - 06/30/2026
Mapelli, A.; Massi, M.C.; Cuccuru, G.; Di Angelantonio, E.; Ieva, F.
Prior-informed conditional Gaussian graphical models: an application to protein interaction network reconstruction | Abstract | | Motivation: Protein-protein interaction (PPI) networks, estimated from high-throughput omics data, foster biomarker discovery and precision medicine. Gaussian graphical models (GGMs) offer a principled reconstruction framework. Yet, existing applications face two limitations: they overlook the rich existing knowledge encoded in curated biological databases, and they assume a homogeneous network structure across all individuals, neglecting the influence of covariates or confounding factors on these interactions and preventing personalised representations. Even though these limitations have been addressed separately in previous work, no current approach resolves them simultaneously.
Results: We introduce a prior-informed conditional Gaussian graphical model that integrates database-derived interaction priors with covariate-dependent network modeling in a unified, scalable framework. The key methodological innovation is a structured, weighted penalty that selectively incorporates priors into population-level network estimation, while leaving context-specific perturbations entirely data-driven, as curated databases capture canonical interactions rather than disease-specific signals. Simulation studies demonstrate consistent and robust improvements in population-level network reconstruction across diverse settings, even when prior knowledge is imperfect. Applied to UK Biobank cardiometabolic proteomics (n = 49,129, p = 366 proteins), the method recovers T2D-associated network perturbations, identifying 34 network-central candidate biomarkers, several detectable only through their connectivity, not differential expression, and revealing six biologically coherent protein communities with distinct pathway enrichments spanning metabolic, cardiovascular, and cancer-related processes.
Availability and implementation: Code is available at https://github.com/AlessiaMapelli/Prior-informed-conditional-GGMs. |
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57/2026 - 06/29/2026
Fontana, N.; Secchi, P.; Di Angelantonio, E.; Ieva, F.
Modeling time-varying genetic effects on binary disease risk via functional Mendelian Randomization | Abstract | | Motivation: Genome-wide association studies have identified thousands of genetic variants associated with complex traits, establishing Mendelian Randomization (MR) as a powerful framework for causal inference using variants as natural experiments. However, existing MR methods treat causal effects as static, relying on cross-sectional exposure measurements and ignoring how genetic predispositions to disease operate dynamically across the life course. Recovering age-specific causal effect functions from longitudinal data requires combining functional data representations of exposure trajectories with instrumental variable estimation strategies suitable for binary disease endpoints, a methodological gap that has remained unaddressed.
Results: We develop a functional MR framework for binary outcomes that integrates Functional Principal Component Analysis with Two-Stage Residual Inclusion (2SRI), ensuring consistent estimation under the nonlinear logistic link function that renders standard instrumental variable estimators inconsistent. Simulations across different causal effect trajectory shapes, varying measurement densities, and varying instrument strengths demonstrate accurate recovery of time-varying genetically predicted effects with minimal bias. Applied to UK Biobank data, the framework identifies an age-specific causal effect of genetically predicted body mass index on type 2 diabetes risk concentrated in early mid-adulthood and progressively attenuating thereafter. Concordance between the proposed 2SRI estimator applied to type 2 diabetes and the established continuous-outcome functional MR estimator applied to the paired glycated haemoglobin marker in the same cohort provides indirect empirical support for the validity of the proposed approach.
Availability and implementation: The method is implemented in the R package mvfmr, with a full tutorial vignette. |
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