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 1249 products
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35/2025 - 06/11/2025
Perotto, S.; Ferro, N.; Speroni, G.; Temellini, E.
Anisotropic recovery-based error estimators and mesh adaptation for real-life engineering innovation | Abstract | | This chapter presents an overview of anisotropic mesh adaptation techniques driven by recovery-based a posteriori error estimators. The first part outlines the theoretical foundation for anisotropic error estimation and the construction of metric-based adapted meshes in a steady context. The methodology is then extended to time-dependent problems by coupling mesh adaptation with adaptive time stepping, in a unified space-time framework. The approach is tested on three representative engineering applications, namely structural topology optimization, microstructured material design, and unsteady fluid dynamics, demonstrating the effectiveness in capturing directional features in space and heterogeneities in time. The proposed strategy offers practical advantages in terms of computational efficiency, broad applicability, and ease of integration into existing numerical solvers. |
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34/2025 - 06/07/2025
Bucelli, M.; Dede', L.
Coupling models of resistive valves to muscle mechanics in cardiac fluid-structure interaction simulations | Abstract | | To accurately simulate all phases of the cardiac cycle, computational models of hemodynamics in heart chambers need to include a sufficiently faithful model of cardiac valves. This can be achieved efficiently through resistive methods, and the resistive immersed implicit surface (RIIS) model in particular [Fedele et al., BMMB, 2017]. However, the conventional RIIS model is not suited to fluid-structure interaction (FSI) simulations, since it neglects the reaction forces by which valves are attached to the cardiac walls, leading to models that are not consistent with Newton's laws. In this paper, we propose an improvement to RIIS to overcome this limitation, by adding distributed forces acting on the structure to model the attachment of valves to the cardiac walls. The modification has a minimal computational overhead thanks to an explicit numerical discretization scheme. Numerical experiments in both idealized and realistic settings demonstrate the effectiveness of the proposed modification in ensuring the physical consistency of the model, thus allowing to apply RIIS and other resistive valve models in the context of FSI simulations. |
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32/2025 - 05/28/2025
De Sanctis, M.F.; Di Battista, I.; Arnone, E.; Castiglione, C.; Palummo, A.; Bernardi, M.; Ieva, F.; Sangalli, L.M.
Exploring nitrogen dioxide spatial concentration via physics-informed multiple quantile regression | Abstract | | Understanding the spatial distribution of air pollutants, such as nitrogen dioxide (NO2), is crucial for assessing environmental and health impacts, particularly in densely populated and industrialized regions. This paper introduces a novel method for estimating multiple spatial quantiles, ensuring the monotonicity of the resulting estimates. The proposed model builds upon recent advancements in quantile regression, and incorporates physical information of the phenomenon under analysis, to address the challenges posed by anisotropy, non-stationarity and skewness, typically observed in environmental data. For instance, in the study of air pollutants concentration, the model permits the inclusion of information concerning air-circulation, and in particular the physics of wind streams, which strongly influences the pollutant concentration. Moreover, the monotone estimation of the quantile maps yields a fully nonparametric reconstruction of the pollutant probability density function, at any spatial location. This in turn enables the construction of probability maps, that quantify the likelihood of exceeding regulatory thresholds set by policymakers, offering valuable information for environmental monitoring policies, aimed at mitigating the adverse effects of air pollution. |
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33/2025 - 05/28/2025
Di Battista, I.; De Sanctis, M.F.; Arnone, E.; Castiglione, C.; Palummo, A.; Sangalli, L.M.
A semiparametric space-time quantile regression model | Abstract | | Spatio-temporal data often exhibit non-Gaussian behaviour, heteroscedasticity and skeweness. Such data are, for example, highly prevalent in environmental and ecological sciences. In this work, we propose a semiparametric model for space-time quantile regression. The estimation functional incorporates roughness penalties based on differential operators over both the spatial and temporal dimensions. We study the theoretical properties of the model, proving the consistency and asymptotic normality of the associated estimators. To evaluate the effectiveness of the proposed method, we conduct simulation studies, bench-marking it against state-of-the-art techniques. Finally, we apply the model to analyse the space-time evolution of nitrogen dioxide concentration in the Lombardy region (Italy). The analyses of this pollutant are of primarily importance for informing policies aimed at improving air quality. |
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30/2025 - 05/22/2025
Rosafalco, L.; Conti, P.; Manzoni, A.; Mariani, S.; Frangi, A.
Online learning in bifurcating dynamic systems via SINDy and Kalman filtering | Abstract | | We propose the use of the Extended Kalman Filter (EKF) for online data assimilation and update of a dynamic model, preliminary identified through the Sparse Identification of Nonlinear Dynamics (SINDy). This data-driven technique may avoid biases due to incorrect modelling assumptions and exploits SINDy to approximate the system dynamics leveraging a predefined library of functions, where active terms are selected and weighted by a sparse set of coefficients. This results in a physically-sound and interpretable dynamic model allowing to reduce epistemic uncertainty often affecting machine learning approaches. Treating the SINDy model coefficients as random variables, we propose to update them while acquiring (possibly noisy) system measurements, thus enabling the online identification of time-varying systems. These changes can stem from, e.g., varying operational conditions or unforeseen events. The EKF performs model adaptation through joint state-parameters estimation, with the Jacobian matrices required to computed the model sensitivity inexpensively evaluated from the SINDy model formulation. The effectiveness of this approach is demonstrated through three case studies: (i) a Lotka-Volterra model in which all parameters simultaneously evolve during the observation period; (ii) a Selkov model where the system undergoes a bifurcation not seen during the SINDy training; (iii) a MEMS arch exhibiting a 1:2 internal resonance. The ability of EKF of recovering inactivated functional terms from the SINDy library, or discarding unnecessary contribution, is also highlighted. Based on the presented applications, this method shows strong promise for handling time-varying nonlinear dynamic systems possibly experiencing bifurcating behaviors. |
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31/2025 - 05/22/2025
Botteghi, N.; Fresca, S.; Guo, M.; Manzoni, A.
HypeRL: Parameter-Informed Reinforcement Learning for Parametric PDEs | Abstract | | In this work, we devise a new, general-purpose reinforcement learning strategy for the optimal control of parametric partial differential equations (PDEs). Such problems frequently arise in applied sciences and engineering and entail a significant complexity when control and or state variables are distributed in high- dimensional space or depend on varying parameters. Traditional numerical methods, relying on either iterative minimization algorithms - exploiting, e.g., the solution of the adjoint problem - or dynamic programming - also involving the solution of the Hamilton-Jacobi-Bellman (HJB) equation - while reliable, often become computationally infeasible. Indeed, in either way, the optimal control problem has to be solved for each instance of the parameters, and this is out of reach when dealing with high-dimensional time-dependent and parametric PDEs. In this paper, we propose HypeRL, a deep reinforcement learning (DRL) framework to overcome the limitations shown by traditional methods. HypeRL aims at approximating the optimal control policy directly, bypassing the need to numerically solve the HJB equation explicitly for all possible states and parameters, or solving an adjoint problem within an iterative optimization loop for each parameter instance. Specifically, we employ an actor-critic DRL approach to learn an optimal feedback control strategy that can generalize across the range of variation of the parameters. To effectively learn such optimal control laws for different instances of the parameters, encoding the parameter information into the DRL policy and value function neural networks (NNs) is essential. To do so, HypeRL uses two additional NNs, often called hypernetworks, to learn the weights and biases of the value function and the policy NNs. In this way, HypeRL effectively embeds the parametric information into the value function and policy NNs. We validate the proposed approach on two PDE-constrained optimal control benchmarks, namely a 1D Kuramoto-Sivashinsky equation with in-domain control and on a 2D Navier Stokes equations with boundary control, by showing that the knowledge of the PDE parameters and how this information is encoded, i.e., via a hypernetwork, is an essential ingredient for learning parameter-dependent control policies that can generalize effectively to unseen scenarios and for improving the sample efficiency of such policies. |
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29/2025 - 05/18/2025
Centofanti, E.; Ziarelli, G.; Parolini, N.; Scacchi, S.; Verani, M. ; Pavarino, L. F.
Learning cardiac activation and repolarization times with operator learning | Abstract | | Solving partial or ordinary differential equation models in cardiac electrophysiology is a computationally
demanding task, particularly when high-resolution meshes are required to capture
the complex dynamics of the heart. Moreover, in clinical applications, it is essential to employ
computational tools that provide only relevant information, ensuring clarity and ease of interpretation.
In this work, we exploit two recently proposed operator learning approaches, namely
Fourier Neural Operators (FNO) and Kernel Operator Learning (KOL), to learn the operator
mapping the applied stimulus in the physical domain into the activation and repolarization time
distributions. These data-driven methods are evaluated on synthetic 2D and 3D domains, as well
as on a physiologically realistic left ventricle geometry. Notably, while the learned map between
the applied current and activation time has its modelling counterpart in the Eikonal model, no
equivalent partial differential equation (PDE) model is known for the map between the applied
current and repolarization time. Our results demonstrate that both FNO and KOL approaches
are robust to hyperparameter choices and computationally efficient compared to traditional PDEbased
Monodomain models. These findings highlight the potential use of these surrogate operators
to accelerate cardiac simulations and facilitate their clinical integration. |
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28/2025 - 05/10/2025
Ciaramella, G.; Gander, M.J.; Mazzieri, I.
Discontinuous Galerkin time integration for second-order differential problems: formulations, analysis, and analogies | Abstract | | We thoroughly investigate Discontinuous Galerkin (DG) discretizations as time integrators for second-order oscillatory systems, considering both second-order and first-order formulations of the original problem. Key contributions include new convergence analyses for the second-order formulation and equivalence proofs between DG and classical time-stepping schemes (such as Newmark schemes and general linear methods). In addition, the chapter provides a detailed review and convergence analysis for the first-order formulation, alongside comparisons of the proposed schemes in terms of accuracy, consistency, and computational cost |
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