Luca Franco Pavarino

Edoardo Centofanti, Giovanni Ziarelli, Simone Scacchi et al.

Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness and the prohibitive computational complexity of PDE-constrained optimization. In this work, we introduce a data-driven framework leveraging Latent Dynamics Networks (LDNets) to construct efficient surrogate models of the forward operator. By mapping low-dimensional parameters, representing ectopic activation sites or ischemic region descriptors, to the ECG signals via latent dynamics governed by neural ordinary differential equations, our approach circumvents the computational burden of evaluating high-fidelity cardiac models during iterative parameter estimation. The surrogate is trained offline on high-fidelity data, enabling rapid and robust inversion. We validate the proposed framework through rigorous numerical experiments with synthetic data across both 2d and 3d geometries. Results show that the LDNet-based surrogate achieves precise reconstruction of cardiac parameters while drastically reducing computational overhead, thereby enabling near real-time clinical applications.

Luca Pellegrini, Massimiliano Ghiotto, Edoardo Centofanti et al.

Ionic models, described by systems of stiff ordinary differential equations, are fundamental tools for simulating the complex dynamics of excitable cells in both Computational Neuroscience and Cardiology. Approximating these models using Artificial Neural Networks poses significant challenges due to their inherent stiffness, multiscale nonlinearities, and the wide range of dynamical behaviors they exhibit, including multiple equilibrium points, limit cycles, and intricate interactions. While in previous studies the dynamics of the transmembrane potential has been predicted in low dimensionality settings, in the present study we extend these results by investigating whether Fourier Neural Operators can effectively learn the evolution of all the state variables within these dynamical systems in higher dimensions. We demonstrate the effectiveness of this approach by accurately learning the dynamics of three well-established ionic models with increasing dimensionality: the two-variable FitzHugh-Nagumo model, the four-variable Hodgkin-Huxley model, and the forty-one-variable O'Hara-Rudy model. To ensure the selection of near-optimal configurations for the Fourier Neural Operator, we conducted automatic hyperparameter tuning under two scenarios: an unconstrained setting, where the number of trainable parameters is not limited, and a constrained case with a fixed number of trainable parameters. Both constrained and unconstrained architectures achieve comparable results in terms of accuracy across all the models considered. However, the unconstrained architecture required approximately half the number of training epochs to achieve similar error levels, as evidenced by the loss function values recorded during training. These results underline the capabilities of Fourier Neural Operators to accurately capture complex multiscale dynamics, even in high-dimensional dynamical systems.