arXiv subjects

Simone Pezzuto

Publications and source records attributed to Simone Pezzuto.

At least 19 recordsLinked to original sources

arXiv2026

iLogMap: Geodesic Polar Coordinates Parameterization with the Magnetic Laplacian

Geodesic polar coordinates (GPCs) provide an intrinsic parameterization over curved surfaces, but their accurate estimation remains challenging, particularly in the presence of anisotropic metrics, high curvature and complex topology. We introduce iLogMap, a method for computing GPCs in curved domains that recasts the angular component of the logarithmic map to a ground-state magnetic eigenproblem over the circumferential direction field of geodesic distance. Our method effortlessly extends to anisotropic metric tensors and solid volumes, enabling cylindrical and spherical parameterizations in tetrahedral meshes. Experiments on diverse shapes with varying genus confirm competitive angular accuracy and reduced metric distortion relative to heat-based methods, with improved performance on surfaces with boundary and domains with anisotropy. We demonstrate the utility of iLogMap in computational cardiology applications, where we use it to initialize spiral phases on atrial surfaces and estimate local activation patterns in ventricular models.

cs.CG↗

arXiv2026

Uncertainty Quantification for Cardiac Shape Reconstruction with Deep Signed Distance Functions via MCMC methods

Atlas-based approaches allow high-quality, patient-specific shape reconstructions of cardiac anatomy from sparse and/or noisy data such as point clouds. However, these methods are mainly prior-driven, so the impact of uncertainty can be large, limiting their clinical reliability. We propose a probabilistic framework for uncertainty-aware cardiac shape reconstruction that combines Deep Signed Distance Functions (DeepSDFs) with Markov Chain Monte Carlo (MCMC) sampling. Cardiac geometries are modeled implicitly as zero-level sets of a neural network conditioned on learned latent codes, enabling multi-surface reconstruction of the left and right ventricles. By interpreting the reconstruction loss as a log-likelihood, we perform Bayesian inference in the latent space to obtain both maximum a posteriori (MAP) and posterior-sampled reconstructions. Experiments on a public cardiac dataset show that our approach produces accurate reconstructions and well-calibrated uncertainty estimates.

eess.IV↗

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{\deg}) 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↗

arXiv2026

Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging

Electrocardiographic imaging (ECGI) seeks to reconstruct cardiac electrical activity from body-surface potentials noninvasively. However, the associated inverse problem is severely ill-posed and requires robust regularization. While classical approaches primarily employ spatial smoothing, the temporal structure of cardiac dynamics remains underexploited despite its physiological relevance. We introduce a space-time regularization framework that couples spatial regularization with a learned temporal Fields-of-Experts (FoE) prior to capture complex spatiotemporal activation patterns. We derive a finite element discretization on unstructured cardiac surface meshes, prove Mosco-convergence, and develop a scalable optimization algorithm capable of handling the FoE term. Numerical experiments on synthetic epicardial data demonstrate improved denoising and inverse reconstructions compared to handcrafted spatiotemporal methods, yielding solutions that are both robust to noise and physiologically plausible.

math.NA↗

arXiv2026

NET4EXA: Pioneering the Future of Interconnects for Supercomputing and AI

NET4EXA aims to develop a next-generation high-performance interconnect for HPC and AI systems, addressing the increasing demands of large-scale infrastructures, such as those required for training Large Language Models. Building upon the proven BXI (Bull eXascale Interconnect) European technology used in TOP15 supercomputers, NET4EXA will deliver the new BXI release, BXIv3, a complete hardware and software interconnect solution, including switch and network interface components. The project will integrate a fully functional pilot system at TRL 8, ready for deployment into upcoming exascale and post-exascale systems from 2025 onward. Leveraging prior research from European initiatives like RED-SEA, the previous achievements of consortium partners and over 20 years of expertise from BULL, NET4EXA also lays the groundwork for the future generation of BXI, BXIv4, providing analysis and preliminary design. The project will use a hybrid development and co-design approach, combining commercial switch technology with custom IP and FPGA-based NICs. Performances of NET4EXA BXIv3 interconnect will be evaluated using a broad portfolio of benchmarks, scientific scalable applications, and AI workloads.

cs.NI↗

arXiv2024

Accurate and Efficient Cardiac Digital Twin from surface ECGs: Insights into Identifiability of Ventricular Conduction System

Digital twins for cardiac electrophysiology are an enabling technology for precision cardiology. Current forward models are advanced enough to simulate the cardiac electric activity under different pathophysiological conditions and accurately replicate clinical signals like torso electrocardiograms (ECGs). In this work, we address the challenge of matching subject-specific QRS complexes using anatomically accurate, physiologically grounded cardiac digital twins. By fitting the initial conditions of a cardiac propagation model, our non-invasive method predicts activation patterns during sinus rhythm. For the first time, we demonstrate that distinct activation maps can generate identical surface ECGs. To address this non-uniqueness, we introduce a physiological prior based on the distribution of Purkinje-muscle junctions. Additionally, we develop a digital twin ensemble for probabilistic inference of cardiac activation. Our approach marks a significant advancement in the calibration of cardiac digital twins and enhances their credibility for clinical application.

math.OC↗

arXiv2024

Ensemble learning of the atrial fiber orientation with physics-informed neural networks

The anisotropic structure of the myocardium is a key determinant of the cardiac function. To date, there is no imaging modality to assess in-vivo the cardiac fiber structure. We recently proposed Fibernet, a method for the automatic identification of the anisotropic conduction -- and thus fibers -- in the atria from local electrical recordings. Fibernet uses cardiac activation as recorded during electroanatomical mappings to infer local conduction properties using physics-informed neural networks. In this work, we extend Fibernet to cope with the uncertainty in the estimated fiber field. Specifically, we use an ensemble of neural networks to produce multiple samples, all fitting the observed data, and compute posterior statistics. We also introduce a methodology to select the best fiber orientation members and define the input of the neural networks directly on the atrial surface. With these improvements, we outperform the previous methodology in terms of fiber orientation error in 8 different atrial anatomies. Currently, our approach can estimate the fiber orientation and conduction velocities in under 7 minutes with quantified uncertainty, which opens the door to its application in clinical practice. We hope the proposed methodology will enable further personalization of cardiac digital twins for precision medicine.

cs.LG↗

arXiv2024

An eikonal model with re-excitability for fast simulations in cardiac electrophysiology

Precision cardiology based on cardiac digital twins requires accurate simulations of cardiac arrhythmias. However, detailed models, such as the monodomain model, are computationally costly and have limited applicability in practice. Thus, it desirable to have fast models that can still represent the main physiological features presented during cardiac arrhythmias. The eikonal model is an approximation of the monodomain model that is widely used to describe the arrival times of the electrical wave. However, the standard eikonal model does not generalize to the complex re-entrant dynamics that characterize the cardiac arrhythmias. In this work, we propose an eikonal model that includes the tissue re-excitability, which allows to describe re-entries. The re-excitability properties are inferred from the monodomain model. Our eikonal model also handles the tissue anisotropy and heterogeneity. We compare the eikonal model to the monodomain model in various numerical experiments in the atria and the ventricles. The eikonal model is qualitatively accurate in the simulation of re-entries and can be potentially ran in real-time, opening the door to its clinical applicability.

cs.CE↗

arXiv2024

Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging

Reconstructing cardiac electrical activity from body surface electric potential measurements results in the severely ill-posed inverse problem in electrocardiography. Many different regularization approaches have been proposed to improve numerical results and provide unique results. This work presents a novel approach for reconstructing the epicardial potential from body surface potential maps based on a space-time total variation-type regularization using finite elements, where a first-order primal-dual algorithm solves the underlying convex optimization problem. In several numerical experiments, the superior performance of this method and the benefit of space-time regularization for the reconstruction of epicardial potential on two-dimensional torso data and a three-dimensional rabbit heart compared to state-of-the-art methods are demonstrated.

math.NA↗

arXiv2024

High-order parallel-in-time method for the monodomain equation in cardiac electrophysiology

Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by distributing the computational load more effectively, time parallelization is essential. We introduce a high-order parallel-in-time method addressing the substantial computational challenges posed by the stiff, multiscale, and nonlinear nature of cardiac dynamics. Our method combines the semi-implicit and exponential spectral deferred correction methods, yielding a hybrid method that is extended to parallel-in-time employing the PFASST framework. We thoroughly evaluate the stability, accuracy, and robustness of the proposed parallel-in-time method through extensive numerical experiments, using practical ionic models such as the ten-Tusscher-Panfilov. The results underscore the method's potential to significantly enhance real-time and high-fidelity simulations in biomedical research and clinical applications.

math.NA↗

arXiv2024

Reconstruction of the local contractility of the cardiac muscle from deficient apparent kinematics

Active solids are a large class of materials, including both living soft tissues and artificial matter, that share the ability to undergo strain even in absence of external loads. While in engineered materials the actuation is typically designed a priori, in natural materials it is an unknown of the problem. In such a framework, the identification of inactive regions in active materials is of particular interest. An example of paramount relevance is cardiac mechanics and the assessment of regions of the cardiac muscle with impaired contractility. The impossibility to measure the local active forces directly suggests us to develop a novel methodology exploiting kinematic data from clinical images by a variational approach to reconstruct the local contractility of the cardiac muscle. By finding the stationary points of a suitable cost functional we recover the contractility map of the muscle. Numerical experiments, including severe conditions with added noise to model uncertainties, and data knowledge limited to the boundary, demonstrate the effectiveness of our approach. Unlike other methods, we provide a spatially continuous recovery of the contractility map without compromising the computational efficiency.

physics.med-ph↗

arXiv2024

Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology

Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.

math.NA↗

arXiv2023

Probabilistic learning of the Purkinje network from the electrocardiogram

The identification of the Purkinje conduction system in the heart is a challenging task, yet essential for a correct definition of cardiac digital twins for precision cardiology. Here, we propose a probabilistic approach for identifying the Purkinje network from non-invasive clinical data such as the standard electrocardiogram (ECG). We use cardiac imaging to build an anatomically accurate model of the ventricles; we algorithmically generate a rule-based Purkinje network tailored to the anatomy; we simulate physiological electrocardiograms with a fast model; we identify the geometrical and electrical parameters of the Purkinje-ECG model with Bayesian optimization and approximate Bayesian computation. The proposed approach is inherently probabilistic and generates a population of plausible Purkinje networks, all fitting the ECG within a given tolerance. In this way, we can estimate the uncertainty of the parameters, thus providing reliable predictions. We test our methodology in physiological and pathological scenarios, showing that we are able to accurately recover the ECG with our model. We propagate the uncertainty in the Purkinje network parameters in a simulation of conduction system pacing therapy. Our methodology is a step forward in creation of digital twins from non-invasive data in precision medicine. An open source implementation can be found at http://github.com/fsahli/purkinje-learning

stat.ML↗

arXiv2023

Shape of my heart: Cardiac models through learned signed distance functions

The efficient construction of anatomical models is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned to model the spatial relation of multiple chambers. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as the electroanatomical mapping (EAM).

eess.IV↗

arXiv2023

Digital twinning of cardiac electrophysiology models from the surface ECG: a geodesic backpropagation approach

The eikonal equation has become an indispensable tool for modeling cardiac electrical activation accurately and efficiently. In principle, by matching clinically recorded and eikonal-based electrocardiograms (ECGs), it is possible to build patient-specific models of cardiac electrophysiology in a purely non-invasive manner. Nonetheless, the fitting procedure remains a challenging task. The present study introduces a novel method, Geodesic-BP, to solve the inverse eikonal problem. Geodesic-BP is well-suited for GPU-accelerated machine learning frameworks, allowing us to optimize the parameters of the eikonal equation to reproduce a given ECG. We show that Geodesic-BP can reconstruct a simulated cardiac activation with high accuracy in a synthetic test case, even in the presence of modeling inaccuracies. Furthermore, we apply our algorithm to a publicly available dataset of a biventricular rabbit model, with promising results. Given the future shift towards personalized medicine, Geodesic-BP has the potential to help in future functionalizations of cardiac models meeting clinical time constraints while maintaining the physiological accuracy of state-of-the-art cardiac models.

math.OC↗

arXiv2023

Boundary Integral Formulation of the Cell-by-Cell Model of Cardiac Electrophysiology

We propose a boundary element method for the accurate solution of the cell-by-cell bidomain model of electrophysiology. The cell-by-cell model, also called Extracellular-Membrane-Intracellular (EMI) model, is a system of reaction-diffusion equations describing the evolution of the electric potential within each domain: intra- and extra-cellular space and the cellular membrane. The system is parabolic but degenerate because the time derivative is only in the membrane domain. In this work, we adopt a boundary-integral formulation for removing the degeneracy in the system and recast it to a parabolic equation on the membrane. The formulation is also numerically advantageous since the number of degrees of freedom is sensibly reduced compared to the original model. Specifically, we prove that the boundary-element discretization of the EMI model is equivalent to a system of ordinary differential equations, and we consider a time discretization based on the multirate explicit stabilized Runge-Kutta method. We numerically show that our scheme convergences exponentially in space for the single-cell case. We finally provide several numerical experiments of biological interest.

math.NA↗

arXiv2022

$\Delta$-PINNs: physics-informed neural networks on complex geometries

Physics-informed neural networks (PINNs) have demonstrated promise in solving forward and inverse problems involving partial differential equations. Despite recent progress on expanding the class of problems that can be tackled by PINNs, most of existing use-cases involve simple geometric domains. To date, there is no clear way to inform PINNs about the topology of the domain where the problem is being solved. In this work, we propose a novel positional encoding mechanism for PINNs based on the eigenfunctions of the Laplace-Beltrami operator. This technique allows to create an input space for the neural network that represents the geometry of a given object. We approximate the eigenfunctions as well as the operators involved in the partial differential equations with finite elements. We extensively test and compare the proposed methodology against traditional PINNs in complex shapes, such as a coil, a heat sink and a bunny, with different physics, such as the Eikonal equation and heat transfer. We also study the sensitivity of our method to the number of eigenfunctions used, as well as the discretization used for the eigenfunctions and the underlying operators. Our results show excellent agreement with the ground truth data in cases where traditional PINNs fail to produce a meaningful solution. We envision this new technique will expand the effectiveness of PINNs to more realistic applications.

cs.LG↗