Publication
PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology
Publications associées (50)
A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart
We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our mod ...
WILEY2023Low-Rank Tensor Methods for High-Dimensional Problems
In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...
EPFL2023lifex-ep: a robust and efficient software for cardiac electrophysiology simulations
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Background: 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 ...
London2023Learning Dynamics of Spring-Mass Models with Physics-Informed Graph Neural Networks
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The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...
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SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS2022Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations
This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
EPFL2021Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations
In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...
EPFL2021Efficient algorithms for wave problems
Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...
EPFL2021POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium
Alfio Quarteroni, Andrea Manzoni
The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) ...
FRONTIERS MEDIA SA2021