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 1313 prodotti
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54/2025 - 08/09/2025
Tomasetto, M.; Williams, J.P.; Braghin, F.; Manzoni, A.; Kutz, J.N.
Reduced order modeling with shallow recurrent decoder networks | Abstract | | Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control. However, conventional dimensionality reduction techniques are typically limited to known and constant parameters, inefficient for nonlinear and chaotic dynamics, and uninformed to the actual system behavior. In this work, we propose sensor-driven SHallow REcurrent Decoder networks for Reduced Order Modeling (SHRED-ROM). Specifically, we consider the composition of a long short-term memory network, which encodes the temporal dynamics of limited sensor data in multiple scenarios, and a shallow decoder, which reconstructs the corresponding high-dimensional states. SHRED-ROM is a robust decoding-only strategy that circumvents the numerically unstable approximation of an inverse which is required by encoding-decoding schemes. To enhance computational efficiency and memory usage, the full-order state snapshots are reduced by, e.g., proper orthogonal decomposition, allowing for compressive training of the networks with minimal hyperparameter tuning. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED ROM (i) accurately reconstructs the state dynamics for new parameter values starting from limited fixed or mobile sensors, independently on sensor placement, (ii) can cope with both physical, geometrical and time dependent parametric dependencies, while being agnostic to their actual values, (iii) can accurately estimate unknown parameters, and (iv) can deal with different data sources, such as high-fidelity simulations, coupled fields and videos. |
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53/2025 - 08/09/2025
Zecchi, A. A.; Sanavio, C.; Perotto, S.; Succi, S.
Telescopic quantum simulation of the advection-diffusion-reaction dynamics | Abstract | | Quantum singular value transformation (QSVT) is a powerful technique that applies a polynomial transformation to the singular values of a matrix encoded in a unitary operator. Many quantum algorithms can be viewed as a particular application of this technique, though its application to the quantum computation of classical dynamics has not been extensively explored. We introduce a telescopic quantum algorithm for solving the advection-diffusion-reaction (ADR) equation at a given (possibly large) final simulation time, applying the QSVT to an efficient block-encoding of the matrix representing the considered dynamics. We decompose the ADR time evolution function using a Chebyshev polynomial of degree d and we show that effectively exploiting the spectral knowledge of the input matrix within the QSVT protocol can provide a similar simulation error with up to an order of magnitude lower of polynomial degree.
The associated quantum circuit employs only n+4 qubits where N=2^n is the number of spatial discretization points, and achieves circuit depth of O(d × poly(n)). The efficient use of quantum resources and the reduced overall complexity pave the way for the application of the proposed algorithm on near term quantum hardware.
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55/2025 - 08/09/2025
Gimenez Zapiola, A.; Boselli, A.; Menafoglio, A.; Vantini, S.
Hyper-spectral Unmixing algorithms for remote compositional surface mapping: a review of the state of the art | Abstract | | This work concerns a detailed review of data analysis methods used for remotely sensed images of large areas of the Earth and of other solid astronomical objects. In detail, it focuses on the problem of inferring the materials that cover the surfaces captured by hyper-spectral images and estimating their abundances and spatial distributions within the region. The most successful and relevant hyper-spectral unmixing methods are reported as well
as compared, as an addition to analysing the most recent methodologies. The most important public data-sets in this setting, which are vastly used in the testing and validation of the former, are also systematically explored. Finally, open problems are spotlighted and concrete recommendations for future research are provided. |
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51/2025 - 04/09/2025
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 - 29/08/2025
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 - 26/08/2025
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 - 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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