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 1268 products
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42/2025 - 07/11/2025
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 - 07/08/2025
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 - 07/08/2025
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 - 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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