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 1275 prodotti
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48/2025 - 20/08/2025
Temellini, E.; Ballarin, F.; Chacon Rebollo, T.; Perotto, S.
On the inf-sup condition for Hierarchical Model reduction of the Stokes problem | Abstract | | Hierarchical Model Reduction is an effective Reduced Order Modelling
technique for problems defined on elongated, pipe-like domains. It is particularly suitable when a dominant dynamics is aligned with the longitudinal direction, while transverse effects are locally significant but spatially limited. When applied to two-field problems such as the Stokes equations, a main challenge is to ensure the stability of the reduced formulation, particularly the inf-sup condition for pressure discretization. In this work, we provide a rigorous analysis showing that the inf-sup condition holds whenever the number of velocity modes is at least equal to the number of pressure modes, thereby extending previous heuristic approaches. The proof exploits the separation of variables in HiMod and is valid for pipe-like domains under some geometric assumptions. Numerical assessment confirms the theoretical findings, providing a solid foundation for stable and efficient HiMod reduction in incompressible flow problems. |
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47/2025 - 13/08/2025
Gimenez Zapiola, A.; Consolo, A.; Amaldi, E.; Vantini, S.
Penalised Optimal Soft Trees for Functional Data | Abstract | | We propose a new tree-based classifier for Functional Data. A novel objective function for Suárez and Lutsko (1999)’s globally-optimised Soft Classification Trees is proposed to adapt it to the Functional Data Analysis setting when using an FPCA basis. It consists of a supervised and an unsupervised term, with the latter working as a penalisation for heterogeneity in the leaf nodes of the tree. Experiments on benchmark data sets and two case studies demonstrate that the penalisation and proposed initialisation heuristics work synergically to increase model performance
both in the train and test data set. In particular, including the unsupervised term shows to aid the supervised term to reach better objective function values. The case studies specifically illustrate how the unsupervised term yields adaptiveness to different problems, by using custom criteria of homogeneity in the leaf nodes. The interpretability of the splitting functions at the internal nodes is also discussed. |
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46/2025 - 11/08/2025
Mirabella, S.; David, E.; Antona, A.; Stanghellini, C.; Ferro, N.; Matteucci, M.; Heuvelink, E.; Perotto, S.
On the Impact of Light Spectrum on Lettuce Biophysics: A Dynamic Growth Model for Vertical Farming | Abstract | | Current crop growth models, whether process-based or data-driven, rarely incorporate spectral light composition, limiting their applicability in highly controlled environments such as vertical farming. This work addresses this gap by adjusting a well-established process-based model for lettuce growth with an explicit, data-driven representation of light spectrum effects. Using explainable machine learning techniques, we identify the most relevant spectral features, specifically the Blue:Red
and FarRed:Red ratios, and integrate them into a new model parameter, which captures their physiological impact on plant development. The resulting adjusted model (aVHopt) is then validated on an independent literature dataset, showing a substantial reduction in prediction error compared to the reference state-of-the-art model, with a more than 60% decrease in RMSE. The application of the aVHopt model to a commercial dataset confirms its capability to capture key spectral effects, but also reveals its sensitivity to environmental and biological variability not fully accounted for in the current formulation. |
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45/2025 - 28/07/2025
Caliò, G.; Ragazzi, F.; Popoli, A.; Cristofolini, A.; Valdettaro, L; De Falco, C.; Barbante, F.
Hierarchical Multiscale Modeling of Positive Corona Discharges | Abstract | | In the field of corona discharges, the complex chemical mechanisms inside the ionization region have prompted the development of simplified models to replicate the macroscopic effects of ion generation, thereby reducing the computational effort, especially in two and three dimensional simulations. We propose a methodology that allows to replace the ionization process with appropriate boundary conditions used by a corona model solving the drift region. We refer to this model as macro-scale, since it does not solve the ionization region. Our approach begins with one dimensional computations in cylindrical coordinates of the whole discharge, where we include a fairly detailed model of the plasma region near the emitter. We refer to this model as full-scale, since all the spatial scales, including the ionization region, are properly taken into account. From these results it is possible to establish boundary conditions for macroscopic simulations. The idea is that, given an emitter radius, the boundary conditions can be used for a variety of geometries that leverage on that emitter as active electrode. Our results agree with available experimental data for positive corona discharges in different configurations and with simplified analytical models from literature. |
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44/2025 - 16/07/2025
Brivio, S.; Fresca, S.; Manzoni, A.
Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROM | Abstract | | Deep Learning-based Reduced Order Models (DL-ROMs) constitute a consolidated class of techniques that aim at providing accurate surrogate models for complex physical systems described by Partial Differential Equations (PDEs) by nonlinearly compressing the solution manifold into a handful of latent coordinates. Until now, the development of DL-ROMs mainly focused on physically parameterized problems. Within this work we provide a novel extension of these architectures to problems featuring geometrical variability and parametrized domains, namely, we propose Continuous Geometry-Aware DL-ROMs (CGA-DL-ROMs). Specifically, we emphasize that the space-continuous nature of the proposed architecture matches the necessity to deal with multi-resolution datasets, which are quite common in the case of geometrically parametrized problems. Moreover, CGA-DL-ROMs are endowed with a strong inductive bias that makes them aware of geometrical parametrization, thus enhancing both the compression capability and the overall performance of the architecture. Within this work we justify our findings through a suitable theoretical analysis and we experimentally validate our claims by means of a series of numerical tests encompassing physically-and-geometrically parametrized differential problems ranging from the unsteady Navier-Stokes equations for fluid dynamics to advection-diffusion-reaction equations for mathematical biology. |
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43/2025 - 14/07/2025
Tomasetto, M.; Manzoni, A.; Braghin, F.
Real-time optimal control of high-dimensional parametrized systems by deep-learning based reduced order models | Abstract | | Steering a system towards a desired target in a very short amount of time is a challenging task from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the state of the physical system to be controlled. Moreover, the control action needs to be updated whenever the underlying scenario undergoes variations, as it often happens in applications. Full-order models based on, e.g., the Finite Element Method, do not meet these requirements due to the computational burden they usually entail. On the other hand, conventional reduced order modeling techniques such as the Reduced Basis method, despite their rigorous construction, are intrusive, rely on a linear superimposition of modes, and lack of efficiency when addressing nonlinear time-dependent dynamics. In this work, we propose a non-intrusive Deep Learning-based Reduced Order Modeling (DL-ROM) technique for the rapid control of systems described in terms of parametrized PDEs in multiple scenarios. In particular, optimal full-order snapshots are generated and properly reduced by either Proper Orthogonal Decomposition or deep autoencoders (or a combination thereof) while feedforward neural networks are exploited to learn the map from scenario parameters to reduced optimal solutions. Nonlinear dimensionality reduction therefore allows us to consider state variables and control actions that are both low-dimensional and distributed. After (i) data generation, (ii) dimensionality reduction, and (iii) neural networks training in the offline phase, optimal control strategies can be rapidly retrieved in an online phase for any scenario of interest. The computational speedup and the extremely high accuracy obtained with the proposed approach are finally assessed on different PDE-constrained optimization problems, ranging from the minimization of energy dissipation in incompressible flows modeled through Navier-Stokes equations to the thermal active cooling in heat transfer. |
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41/2025 - 11/07/2025
Torzoni, M.; Maisto, D.; Manzoni, A.; Donnarumma, F.; Pezzulo, G.; Corigliano, A.
Active digital twins via active inference | Abstract | | Digital twins are transforming engineering and applied sciences by enabling real-time monitoring, simulation, and predictive analysis of physical systems and processes. However, conventional digital twins rely primarily on passive data assimilation, which limits their adaptability in uncertain and dynamic environments. This paper introduces the active digital twin paradigm, based on active inference. Active inference is a neuroscience-inspired, Bayesian framework for probabilistic reasoning and predictive modeling that unifies inference, decision-making, and learning under a unique, free energy minimization objective. By formulating the evolution of the active digital twin as a partially observable Markov decision process, the active inference agent continuously refines its generative model through Bayesian updates and forecasts future states and observations. Decision-making emerges from an optimization process that balances pragmatic exploitation (maximizing goal-directed utility) and epistemic exploration or information gain (actively resolving uncertainty). Actions are dynamically planned to minimize expected free energy, which quantifies both the divergence between predicted and preferred future observations, and the epistemic value of expected information gain about hidden states. This approach enables a new level of autonomy and resilience in digital twins, offering superior spontaneous exploration capabilities. The proposed framework is assessed on the health monitoring and predictive maintenance of a railway bridge. |
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42/2025 - 11/07/2025
Franco, N. R.; Manzoni, A.; Zunino, P.; Hesthaven, J. S.
Deep orthogonal decomposition: a continuously adaptive neural network approach to model order reduction of parametrized partial differential equations | Abstract | | Wedevelop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach involves constructing a deep neural network model that approximates the solution manifold using a continuously adaptive local basis. In contrast to global methods, such as Principal Orthogonal Decomposition (POD), this adaptivity allows the DODtomitigate the Kolmogorov barrier when dealing with space-interacting parameters,
making the approach applicable to a wide spectrum of parametric problems. Leveraging this idea, we use the DOD to construct an adaptive alternative to the so-called POD-NN method, here termed DOD-NN. The approach is fully data-driven and nonintrusive but, at the same time, allows for a tight control on error propagation and remains highly interpretable thanks to the rich structure present in the latent space. For this reason, the proposed approach stands out as a valuable alternative to other nonlinear model order reduction techniques, such
as those based on deep autoencoders. The methodology is discussed both theoretically and practically, evaluating its performances on problems involving nonlinear PDEs, parametrized geometries and high-dimensional parameter spaces. Finally, we conclude with a brief discussion on potential applications of the DOD beyond DOD-NN, featuring, for instance, the integration of our approach within intrusive reduced order models such as the Reduced Basis Method. |
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