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 1255 prodotti
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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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40/2025 - 08/07/2025
Tentori, C.A.; Gregorio, C.; ...; Ieva, F.; Della Porta, M.G.
Clinical and Genomic-Based Decision Support System to Define the Optimal Timing of Allogeneic Hematopoietic Stem-Cell Transplantation in Patients With Myelodysplastic Syndromes | Abstract | | PURPOSE: Allogeneic hematopoietic stem-cell transplantation (HSCT) is the only potentially curative treatment for patients with myelodysplastic syndromes (MDS). Several issues must be considered when evaluating the benefits and risks of HSCT for patients with MDS, with the timing of transplantation being a crucial question. Here, we aimed to develop and validate a decision support system to define the optimal timing of HSCT for patients with MDS on the basis of clinical and genomic information as provided by the Molecular International Prognostic Scoring System (IPSS-M).
PATIENTS AND METHODS: We studied a retrospective population of 7,118 patients, stratified into training and validation cohorts. A decision strategy was built to estimate the average survival over an 8-year time horizon (restricted mean survival time [RMST]) for each combination of clinical and genomic covariates and to determine the optimal transplantation policy by comparing different strategies.
RESULTS Under an IPSS-M based policy, patients with either low and moderate-low risk benefited from a delayed transplantation policy, whereas in those belonging to moderately high-, high- and very high-risk categories, immediate transplantation was associated with a prolonged life expectancy (RMST). Modeling decision analysis on IPSS-M versus conventional Revised IPSS (IPSS-R) changed the transplantation policy in a significant proportion of patients (15% of patient candidate to be immediately transplanted under an IPSS-R–based policy would benefit from a delayed strategy by IPSS-M, whereas 19% of candidates to delayed transplantation by IPSS-R would benefit from immediate HSCT by IPSS-M), resulting in a significant gain-in-life expectancy under an IPSS-M–based policy (P 5 .001).
CONCLUSION These results provide evidence for the clinical relevance of including genomic features into the transplantation decision making process, allowing personalizing the hazards and effectiveness of HSCT in patients with MDS. |
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37/2025 - 08/07/2025
Spreafico, M.; Ieva, F.; Fiocco, M.
Causal effect of chemotherapy received dose intensity on survival outcome: a retrospective study in osteosarcoma | Abstract | | Background This study aims to analyse the effects of reducing Received Dose Intensity (RDI) in chemotherapy treatment for osteosarcoma patients on their survival by using a novel approach. Previous research has highlighted discrepancies between planned and actual RDI, even among patients randomized to the same treatment regimen. To mitigate toxic side effects, treatment adjustments, such as dose reduction or delayed courses, are necessary. Toxicities are therefore risk factors for mortality and predictors of future exposure levels. Toxicity introduces post-assignment confounding when assessing the causal effect of chemotherapy RDI on survival outcomes, a topic of ongoing debate.
Methods Chemotherapy administration data from BO03 and BO06 Randomized Clinical Trials (RCTs) in osteosarcoma are employed to emulate a target trial with three RDI-based exposure strategies: 1) standard, 2) reduced, and 3) highly-reduced RDI. Investigations are conducted between subgroups of patients characterised by poor or good Histological Responses (HRe), i.e., the strongest known prognostic factor for survival in osteosarcoma. Inverse Probability of Treatment Weighting (IPTW) is first used to transform the original population into a pseudo-population which mimics
the target randomized cohort. Then, a Marginal Structural Cox Model with effect modification is employed. Conditional Average Treatment Effects (CATEs) are ultimately measured as the difference between the Restricted Mean Survival Time of reduced/highly-reduced RDI strategy and the standard one. Confidence Intervals for CATEs are obtained
using a novel IPTW-based bootstrap procedure.
Results Significant effect modifications based on HRe were found. Increasing RDI-reductions led to contrasting trends for poor and good responders: the higher the reduction, the better (worsen) was the survival in poor (good) reponders. Due to their intrinsic resistance to chemotherapy, poor reponders could benefit from reduced RDI, with an average gain of 10.2 and 15.4 months at 5-year for reduced and highly-reduced exposures, respectively.
Conclusions This study introduces a novel approach to (i) comprehensively address the challenges related to the analysis of chemotherapy data, (ii) mitigate the toxicity-treatment-adjustment bias, and (iii) repurpose existing RCT data for retrospective analyses extending beyond the original trials’ intended scopes. |
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35/2025 - 11/06/2025
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 - 07/06/2025
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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