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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51/2025 - 09/04/2025
Tomasetto, M.; Braghin, F., Manzoni, A.
Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models | Abstract | | Continuous monitoring and real-time control of high-dimensional distributed systems are often crucial in applications to ensure a desired physical behavior, without degrading stability and system performances. Traditional feedback control design that relies on full-order models, such as high-dimensional state-space representations or partial differential equations, fails to meet these requirements due to the delay in the control computation, which requires multiple expensive simulations of the physical system. The computational bottleneck is even more severe when considering parametrized systems, as new strategies have to be determined for every new scenario. To address these challenges, we propose a real time closed-loop control strategy enhanced by nonlinear non-intrusive Deep Learning-based Reduced Order Models (DL ROMs). Specifically, in the offline phase, (i) full-order state-control pairs are generated for different scenarios through the adjoint method, (ii) the essential features relevant for control design are extracted from the snapshots through a combination of Proper Orthogonal Decomposition (POD) and deep autoencoders, and (iii) the low-dimensional policy bridging latent control and state spaces is approximated with a feedforward neural network. After data generation and neural networks training, the optimal control actions are retrieved in real-time for any observed state and scenario. In addition, the dynamics may be approximated through a cheap surrogate model in order to close the loop at the latent level, thus continuously controlling the system in real-time even when full-order state measurements are missing. The effectiveness of the proposed method, in terms of computational speed, accuracy, and robustness against noisy data, is finally assessed on two different high-dimensional optimal transport problems, one of which also involving an underlying fluid flow. |
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50/2025 - 08/29/2025
Bonetti, S.; Botti, M.; Antonietti, P.F.
Conforming and discontinuous discretizations of non-isothermal Darcy–Forchheimer flows | Abstract | | We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first approach is based on fully discontinuous Galerkin discretization spaces. In contrast, in the second approach, the velocity is approximated in the Raviart-Thomas space, and the pressure and temperature are still piecewise discontinuous. A fixed-point linearization strategy, naturally inducing an iterative splitting solution, is proposed for treating the nonlinearities of the problem. We present a unified stability analysis and prove the convergence of the iterative algorithm under mild requirements on the problem data. A wide set of two- and three-dimensional simulations is presented to assess the error decay and demonstrate the practical performance of the proposed approaches in physically sound test cases. |
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49/2025 - 08/26/2025
Zanin, A.; Pagani, S.; Corti, M.; Crepaldi, V.; Di Fede, G.; Antonietti, P.F.; the ADNI
Predicting Alzheimer's Disease Progression from Sparse Multimodal Data by NeuralODE Models | Abstract | | Alzheimer's disease shows significantly variable progressions between patients, making early diagnosis, disease monitoring, and care planning difficult. Existing data-driven Disease Progression Models try to tackle this issue, but they usually require sufficiently large datasets of specific diagnostic modalities, which are rarely available in clinical practice. Here, we introduce a new modeling framework capable of predicting individual disease trajectories from sparse, irregularly sampled, multi-modal clinical data. Our method uses (recurrent) Neural Ordinary Differential Equations to determine the current hidden state of a patient from sparse past exams and to forecast future disease progression, illustrating how biomarkers evolve over time. When applied to the ADNI clinical cohort, the model detected early signs of disease more accurately than common data-driven alternatives and effectively tracked changes in biomarker trajectories that align with established clinical knowledge. This provides a versatile tool for accurate diagnosis and monitoring of neurodegenerative diseases. |
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48/2025 - 08/20/2025
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 - 08/13/2025
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 - 08/11/2025
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 - 07/28/2025
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 - 07/16/2025
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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