arXiv subjects

Stefano Pagani

Publications and source records attributed to Stefano Pagani.

At least 19 recordsLinked to original sources

arXiv2026

Physics-Informed Neural Networks for the High-Resolution Reconstruction of Flow Measurement Indicators in Fluid Dynamics

Accurate, spatially resolved flow field measurements are essential for the reliable assessment of hemodynamic quantities in cardiovascular research and clinical practice. Experimental techniques, such as 4D flow MRI, PIV, or Doppler ultrasound, often yield data that are sparse, noisy, or under-resolved, particularly near vessel walls and in regions of complex flow. This limits the fidelity of distributed or derived hemodynamic indicators such as the wall shear stress and the clinical utility of such measurements. To address these challenges, we propose a physics-informed neural network (PINN) framework that integrates the incompressible Navier-Stokes equations with velocity measurements coming from experimental flow field data. By embedding physical laws into data, PINN enhances the reconstruction of velocity fields, enables the estimation of unmeasured quantities such as pressure and wall shear stress, and improves the spatial resolution of hemodynamic indicators. We show the effectiveness of our approach using both in silico and experimental data. First, we apply our method to the FDA nozzle benchmark, leveraging both control particle image velocimetry (PIV) measurements and computational fluid dynamics (CFD) simulations. Next, we apply our method to the more complex case of blood flow in an aneurysm model, exploiting in vitro 4D flow MRI data. In both cases, the synergy between data-driven learning and physics-based regularization yields results that align more closely with ground truth observations than standard CFD or pure data-driven approaches. Our findings highlight the potential of PINNs to improve the fidelity of under-resolved flow field measurements and yield spatially resolved hemodynamic indicators.

math.NA↗

arXiv2026

The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods

This work presents a new release of the lymph 2.0 library, an open-source MATLAB framework for high-order discontinuous Galerkin discretizations on general polytopal meshes. The lymph 2.0 version is extended to support discretizations with element-wise polynomial approximation degrees, which allows the design of $p$-adaptive strategies based on a posteriori error indicators. In addition, the library introduces a unified assembly framework that abstracts the construction of discrete operators from the underlying physical model, improving code modularity, parallelism, maintainability, and extensibility. Moreover, the proposed approach enables shared-memory parallelism through dedicated parallel tools. Several numerical examples demonstrate the effectiveness of the proposed developments in reducing the computational cost while preserving approximation accuracy.

math.NA↗

arXiv2026

Physics-constrained identification of graph-based thermal networks for spacecraft digital twins

Reconstructing a thermal model capable of efficiently simulating the behavior of a spacecraft from sparse and localized temperature measurements remains a challenging task. To address this, we introduce a physically-constrained calibration framework for Lumped Parameter Thermal Models (LPTMs), formulated as a trajectory-based inverse problem for graph dynamical systems. The model reconstructs thermal dynamics directly from temperature measurements and known inputs, without relying on a priori parameter values derived from material properties or geometric assumptions. Physical admissibility is enforced at the parameterization level: positivity of nodal coefficients and symmetry of conductive interactions are imposed by construction. This guarantees stable dynamics and restricts the identification problem to a physically meaningful parameter space, improving conditioning without the need of additional regularization. The identification problem is addressed through trajectory matching, ensuring stable rollout over extended time horizons. The methodology is validated on synthetic datasets generated from high-fidelity finite element simulations under progressively complex forcing conditions. The calibrated LPTMs accurately reproduce long-term temperature evolution and exhibit robustness to measurement noise. The proposed framework provides a systematic approach to the calibration of reduced-order thermal models by combining physical structure with data-driven identification. The numerical results show a favorable balance between accuracy and computational efficiency, making the models suitable for integration in spacecraft thermal Digital Twin applications.

math.NA↗

arXiv2026

Mathematical and numerical modeling of coupled oxygen dynamics and neuronal electrophysiology

Modeling and simulating how oxygen supply shapes neuronal excitability is crucial for advancing the understanding of brain function in pathological scenarios, such as ischemia. This condition is caused by a reduced blood supply, leading to the deprivation of oxygen and other metabolites; this energy deficit impairs ionic pumps and causes cellular swelling. In this work, this phenomenon is modeled through a volumetric variation law that links cell swelling to local oxygen concentration and the percentage of blood flow reduction. The swelling law links volume changes to local oxygen and the degree of blood-flow depression, providing a simple mechanistic pathway from hypoxia to tortuosity-driven transport impairment. The interplay between oxygen supply and excitability in brain tissue is described by coupling the monodomain model with specific neuronal ionic and metabolic models that characterize ion and metabolite concentration dynamics. The numerical approximation of this coupled multiscale problem is particularly challenging, owing to the presence of sharp and fast-propagating wavefronts and complex geometrical domains. To address these challenges, suitable space- and time-adaptive schemes are employed to capture the action potential dynamics accurately. This multiscale model is discretized in space with the high-order p-adaptive discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and integrated in time with a Crank-Nicolson scheme. We numerically investigate different pathological scenarios on a two-dimensional idealized square domain and on a realistic geometry, both discretized with a polygonal grid, analyzing how subclinical and severe ischemia can affect brain electrophysiology and metabolic concentrations.

math.NA↗

arXiv2026

Learning geometry-dependent lead-field operators for forward ECG modeling

Modern forward electrocardiogram (ECG) computational models rely on an accurate representation of the torso domain. The lead-field method enables fast ECG simulations while preserving full geometric fidelity. Achieving high anatomical accuracy in torso representation is, however, challenging in clinical practice, as imaging protocols are typically focused on the heart and often do not include the entire torso. In addition, the computational cost of the lead-field method scales linearly with the number of electrodes, limiting its applicability in high-density recording settings. To date, no existing approach simultaneously achieves high anatomical fidelity, low data requirements and computational efficiency. In this work, we propose a shape-informed surrogate model of the lead-field operator that serves as a drop-in replacement for the full-order model in forward ECG simulations. The proposed framework consists of two components: a geometry-encoding module that maps anatomical shapes into a low-dimensional latent space, and a geometry-conditioned neural surrogate that predicts lead-field gradients from spatial coordinates, electrode positions and latent codes. The proposed method achieves high accuracy in approximating lead fields both within the torso (mean angular error 5°) and inside the heart, resulting in highly accurate ECG simulations (relative mean squared error <2.5%. The surrogate consistently outperforms the widely used pseudo lead-field approximation while preserving negligible inference cost. Owing to its compact latent representation, the method does not require a fully detailed torso segmentation and can therefore be deployed in data-limited settings while preserving high-fidelity ECG simulations.

cs.LG↗

arXiv2026

Shape-informed cardiac mechanics surrogates in data-scarce regimes via geometric encoding and generative augmentation

High-fidelity computational models of cardiac mechanics provide mechanistic insight into the heart function but are computationally prohibitive for routine clinical use. Surrogate models can accelerate simulations, but generalization across diverse anatomies is challenging, particularly in data-scarce settings. We propose a two-step framework that decouples geometric representation from learning the physics response, to enable shape-informed surrogate modeling under data-scarce conditions. First, a shape model learns a compact latent representation of left ventricular geometries. The learned latent space effectively encodes anatomies and enables synthetic geometries generation for data augmentation. Second, a neural field-based surrogate model, conditioned on this geometric encoding, is trained to predict ventricular displacement under external loading. The proposed architecture performs positional encoding by using universal ventricular coordinates, which improves generalization across diverse anatomies. Geometric variability is encoded using two alternative strategies, which are systematically compared: a PCA-based approach suitable for working with point cloud representations of geometries, and a DeepSDF-based implicit neural representation learned directly from point clouds. Overall, our results, obtained on idealized and patient-specific datasets, show that the proposed approaches allow for accurate predictions and generalization to unseen geometries, and robustness to noisy or sparsely sampled inputs.

cs.LG↗

arXiv2025

A massively parallel non-overlapping Schwarz preconditioner for PolyDG methods in brain electrophysiology

We investigate non-overlapping Schwarz preconditioners for the algebraic systems stemming from high-order discretizations of the coupled monodomain and Barreto-Cressman models, with applications to brain electrophysiology. The spatial discretization is based on a high-order Polytopal Discontinuous Galerkin (PolyDG) method, coupled with the Crank-Nicolson time discretization scheme with explicit extrapolation of the ion term. To improve solver efficiency, we consider additive Schwarz preconditioners within the PolyDG framework, which combines (massively parallel) local subdomain solvers with a coarse-grid correction. Numerical experiments demonstrate robustness with respect to the discretization parameters, as well as a significant reduction in iteration counts compared to the unpreconditioned solver. These features make the proposed approach well-suited for parallel large-scale simulations in brain electrophysiology.

math.NA↗

arXiv2025

A novel mathematical and computational framework of amyloid-beta triggered seizure dynamics in Alzheimer's disease

The association of epileptic activity and Alzheimer's disease (AD) has been increasingly reported in both clinical and experimental studies, suggesting that amyloid-$β$ accumulation may directly affect neuronal excitability. Capturing these interactions requires a quantitative description that bridges the molecular alterations of AD with the fast electrophysiological dynamics of epilepsy. We introduce a novel mathematical model that extends the Barreto-Cressman ionic formulation by incorporating multiple mechanisms of calcium dysregulation induced by amyloid-$β$, including formation of $\mathrm{Ca}^{2+}$-permeable pores, overactivation of voltage-gated $\mathrm{Ca}^{2+}$ channels, and suppression of $\mathrm{Ca}^{2+}$-sensitive potassium currents. The resulting ionic model is coupled with the monodomain equation and discretized using a $p$-adaptive discontinuous Galerkin method on polytopal meshes, providing an effective balance between efficiency and accuracy in capturing the sharp spatiotemporal electrical wavefronts associated with epileptiform discharges. Numerical simulations performed on idealized and realistic brain geometries demonstrate that progressive amyloid-\textbeta{} accumulation leads to severe alterations in calcium homeostasis, increased neuronal hyperexcitability, and pathological seizure propagation. Specifically, high amyloid-$β$ concentrations produce secondary epileptogenic sources and spatially heterogeneous wavefronts, indicating that biochemical inhomogeneities play a critical role in shaping seizure dynamics. These results illustrate how multiscale modeling provides new mechanistic insights into the interplay between neurodegeneration and epilepsy in Alzheimer's disease.

math.NA↗

arXiv2025

Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs

This work introduces AD-SVFD, a deep learning model for the deformable registration of vascular shapes to a pre-defined reference and for the generation of synthetic anatomies. AD-SVFD operates by representing each geometry as a weighted point cloud and models ambient space deformations as solutions at unit time of ODEs, whose time-independent right-hand sides are expressed through artificial neural networks. The model parameters are optimized by minimizing the Chamfer Distance between the deformed and reference point clouds, while backward integration of the ODE defines the inverse transformation. A distinctive feature of AD-SVFD is its auto-decoder structure, that enables generalization across shape cohorts and favors efficient weight sharing. In particular, each anatomy is associated with a low-dimensional code that acts as a self-conditioning field and that is jointly optimized with the network parameters during training. At inference, only the latent codes are fine-tuned, substantially reducing computational overheads. Furthermore, the use of implicit shape representations enables generative applications: new anatomies can be synthesized by suitably sampling from the latent space and applying the corresponding inverse transformations to the reference geometry. Numerical experiments, conducted on healthy aortic anatomies, showcase the high-quality results of AD-SVFD, which yields extremely accurate approximations at competitive computational costs.

cs.CV↗

arXiv2025

Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models

Active stress models in cardiac biomechanics account for the mechanical deformation caused by muscle activity, thus providing a link between the electrophysiological and mechanical properties of the tissue. The accurate assessment of active stress parameters is fundamental for a precise understanding of myocardial function but remains difficult to achieve in a clinical setting, especially when only displacement and strain data from medical imaging modalities are available. This work investigates, through an in-silico study, the application of physics-informed neural networks (PINNs) for inferring active contractility parameters in time-dependent cardiac biomechanical models from these types of imaging data. In particular, by parametrising the sought state and parameter field with two neural networks, respectively, and formulating an energy minimisation problem to search for the optimal network parameters, we are able to reconstruct in various settings active stress fields in the presence of noise and with a high spatial resolution. To this end, we also advance the vanilla PINN learning algorithm with the use of adaptive weighting schemes, ad-hoc regularisation strategies, Fourier features, and suitable network architectures. In addition, we thoroughly analyse the influence of the loss weights in the reconstruction of active stress parameters. Finally, we apply the method to the characterisation of tissue inhomogeneities and detection of fibrotic scars in myocardial tissue. This approach opens a new pathway to significantly improve the diagnosis, treatment planning, and management of heart conditions associated with cardiac fibrosis.

cs.LG↗

arXiv2025

A p-adaptive polytopal discontinuous Galerkin method for high-order approximation of brain electrophysiology

Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal resolution. This paper introduces a novel p-adaptive discontinuous Galerkin method on polytopal grids (PolyDG) coupled with Crank-Nicolson time integration to approximate such models efficiently. The p-adaptive method enhances local accuracy via dynamic, element-wise polynomial refinement/de-refinement guided by a-posteriori error estimators. A novel clustering algorithm automatizes the selection of elements for adaptive updates, further improving efficiency. A wide set of numerical tests, including epileptic seizure simulations in a sagittal section of a human brain stem, demonstrate the method's ability to reduce computational load while maintaining the accuracy of the numerical solution in capturing the dynamics of multiple wavefronts.

math.NA↗

arXiv2025

Influence of cellular mechano-calcium feedback in numerical models of cardiac electromechanics

Multiphysics and multiscale mathematical models enable the non-invasive study of cardiac function. These models often rely on simplifying assumptions that neglect certain biophysical processes to balance fidelity and computational cost. In this work, we propose an eikonal-based framework that incorporates mechano-calcium feedback -- the effect of mechanical deformation on calcium-troponin buffering -- while introducing only negligible computational overhead. To assess the impact of mechano-calcium feedback at the organ level, we develop a bidirectionally coupled cellular electromechanical model and integrate it into two cardiac multiscale frameworks: a monodomain-driven model that accounts for geometric feedback on electrophysiology and the proposed eikonal-based approach, which instead neglects geometric feedback. By ensuring consistent cellular model calibration across all scenarios, we isolate the role of mechano-calcium feedback and systematically compare its effects against models without it. Our results indicate that, under baseline conditions, mechano-calcium feedback has minimal influence on overall cardiac function. However, its effects become more pronounced in altered force generation scenarios, such as inotropic modulation. Furthermore, we demonstrate that the eikonal-based framework, despite omitting other types of mechano-electric feedback, effectively captures the role of mechano-calcium feedback at significantly lower computational costs than the monodomain-driven model, reinforcing its utility in computational cardiology.

math.NA↗

arXiv2024

A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts

In this work, we aim to formalize a novel scientific machine learning framework to reconstruct the hidden dynamics of the transmission rate, whose inaccurate extrapolation can significantly impair the quality of the epidemic forecasts, by incorporating the influence of exogenous variables (such as environmental conditions and strain-specific characteristics). We propose an hybrid model that blends a data-driven layer with a physics-based one. The data-driven layer is based on a neural ordinary differential equation that learns the dynamics of the transmission rate, conditioned on the meteorological data and wave-specific latent parameters. The physics-based layer, instead, consists of a standard SEIR compartmental model, wherein the transmission rate represents an input. The learning strategy follows an end-to-end approach: the loss function quantifies the mismatch between the actual numbers of infections and its numerical prediction obtained from the SEIR model incorporating as an input the transmission rate predicted by the neural ordinary differential equation. We validate this original approach using both a synthetic test case and a realistic test case based on meteorological data (temperature and humidity) and influenza data from Italy between 2010 and 2020. In both scenarios, we achieve low generalization error on the test set and observe strong alignment between the reconstructed model and established findings on the influence of meteorological factors on epidemic spread. Finally, we implement a data assimilation strategy to adapt the neural equation to the specific characteristics of an epidemic wave under investigation, and we conduct sensitivity tests on the network hyperparameters.

q-bio.QM↗

arXiv2024

Shape-informed surrogate models based on signed distance function domain encoding

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the computational domain. Our approach is based on the combination of two neural networks (NNs). The first NN, conditioned on a latent code, provides an implicit representation of geometry variability through signed distance functions. This automated shape encoding technique generates compact, low-dimensional representations of geometries within a latent space, without requiring the explicit construction of an encoder. The second NN reconstructs the output physical fields independently for each spatial point, thus avoiding the computational burden typically associated with high-dimensional discretizations like computational meshes. Furthermore, we show that accuracy in geometrical characterization can be further enhanced by employing Fourier feature mapping as input feature of the NN. The meshless nature of the proposed method, combined with the dimensionality reduction achieved through automatic feature extraction in latent space, makes it highly flexible and computationally efficient. This strategy eliminates the need for manual intervention in extracting geometric parameters, and can even be applied in cases where geometries undergo changes in their topology. Numerical tests in the field of fluid dynamics and solid mechanics demonstrate the effectiveness of the proposed method in accurately predict the solution of PDEs in domains of arbitrary shape. Remarkably, the results show that it achieves accuracy comparable to the best-case scenarios where an explicit parametrization of the computational domain is available.

math.NA↗

arXiv2024

Physics-informed Neural Network Estimation of Material Properties in Soft Tissue Nonlinear Biomechanical Models

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method and its great potential to enable the robust and effective identification of patient-specific, heterogeneous physical properties, s.a. tissue stiffness properties. In particular, we demonstrate the capability of the PINN to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications.

cs.LG↗

arXiv2024

A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures

Epilepsy is a clinical neurological disorder characterized by recurrent and spontaneous seizures consisting of abnormal high-frequency electrical activity in the brain. In this condition, the transmembrane potential dynamics are characterized by rapid and sharp wavefronts traveling along the heterogeneous and anisotropic conduction pathways of the brain. This work employs the monodomain model, coupled with specific neuronal ionic models characterizing ion concentration dynamics, to mathematically describe brain tissue electrophysiology in grey and white matter at the organ scale. This multiscale model is discretized in space with the high-order discontinuous Galerkin method on polygonal and polyhedral grids (PolyDG) and advanced in time with a Crank-Nicolson scheme. This ensures, on the one hand, efficient and accurate simulations of the high-frequency electrical activity that is responsible for epileptic seizure and, on the other hand, keeps reasonably low the computational costs by a suitable combination of high-order approximations and agglomerated polytopal meshes. We numerically investigate synthetic test cases on a two-dimensional heterogeneous squared domain discretized with a polygonal grid, and on a two-dimensional brainstem in a sagittal plane with an agglomerated polygonal grid that takes full advantage of the flexibility of the PolyDG approximation of the semidiscrete formulation. Finally, we provide a theoretical analysis of stability and an a-priori convergence analysis for a simplified mathematical problem.

math.NA↗

arXiv2023

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors of various research teams, comprehensive and user-friendly software programs for cardiac simulations are still in the process of achieving full maturity within the scientific community. This work introduces lifex-ep, a publicly available software for numerical simulations of the electrophysiology activity of the cardiac muscle, under both physiological and pathological conditions. lifex-ep employs the monodomain equation to model the heart's electrical activity. It incorporates both phenomenological and second-generation ionic models. These models are discretized using the Finite Element method on tetrahedral or hexahedral meshes. Additionally, lifex-ep integrates the generation of myocardial fibers based on Laplace-Dirichlet Rule-Based Methods, previously released in Africa et al., 2023, within lifex-fiber. This paper provides a concise overview of the mathematical models and numerical methods underlying lifex-ep, along with comprehensive implementation details and instructions for users. lifex-ep features exceptional parallel speedup, scaling efficiently when using up to thousands of cores, and its implementation has been verified against an established benchmark problem for computational electrophysiology. We showcase the key features of lifex-ep through various idealized and realistic simulations. lifex-ep offers a user-friendly and flexible interface. lifex-ep provides easy access to cardiac electrophysiology simulations for a wide user community. It offers a computational tool that integrates models and accurate methods for simulating cardiac electrophysiology within a high-performance framework, while maintaining a user-friendly interface.

math.NA↗

arXiv2023

Latent Dynamics Networks (LDNets): learning the intrinsic dynamics of spatio-temporal processes

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to yield predictions through the numerical approximation of high-dimensional systems of differential equations, thus calling for large-scale parallel computing platforms and requiring large computational costs. Data-driven approaches, instead, enable the description of systems evolution in low-dimensional latent spaces, by leveraging dimensionality reduction and deep learning algorithms. We propose a novel architecture, named Latent Dynamics Network (LDNet), which is able to discover low-dimensional intrinsic dynamics of possibly non-Markovian dynamical systems, thus predicting the time evolution of space-dependent fields in response to external inputs. Unlike popular approaches, in which the latent representation of the solution manifold is learned by means of auto-encoders that map a high-dimensional discretization of the system state into itself, LDNets automatically discover a low-dimensional manifold while learning the latent dynamics, without ever operating in the high-dimensional space. Furthermore, LDNets are meshless algorithms that do not reconstruct the output on a predetermined grid of points, but rather at any point of the domain, thus enabling weight-sharing across query-points. These features make LDNets lightweight and easy-to-train, with excellent accuracy and generalization properties, even in time-extrapolation regimes. We validate our method on several test cases and we show that, for a challenging highly-nonlinear problem, LDNets outperform state-of-the-art methods in terms of accuracy (normalized error 5 times smaller), by employing a dramatically smaller number of trainable parameters (more than 10 times fewer).

cs.LG↗