Learning high-dimensional ionic model dynamics using Fourier neural operators

Luca Pellegrini, Massimiliano Ghiotto, Edoardo Centofanti, Luca Franco Pavarino

Abstract: Ionic models, governed by stiff systems of ordinary differential equations characterized by widely separated timescales that make their numerical integration difficult, are key tools for simulating the dynamics of excitable cells in Computational Neuroscience and Cardiology. Approximating these models with Artificial Neural Networks is challenging due to their stiffness associated with multiple timescales, their nonlinearity and the wide range of dynamical behaviors they exhibit such as multiple equilibria, limit cycles, and intricate interactions. While previous studies focused on predicting transmembrane potential in low-dimensional settings, here we investigate whether Fourier Neural Operators (FNOs) can learn the evolution of all state variables in higher-dimensional stiff systems. We evaluate this approach on three representative models of increasing dimensionality: the two-variable FitzHugh–Nagumo model, the four-variable Hodgkin–Huxley model, and the forty-one-variable O’Hara–Rudy model. Beyond accuracy, we examine how system dimensionality affects key performance metrics, including parameter count, training and test errors, memory use, training time, Fourier modes, and network depth. To ensure near-optimal configurations, we performed automatic state-of-the-art hyperparameter tuning in two scenarios: unconstrained and constrained. Both yielded comparable accuracy across all models. These results underline the capabilities of FNOs to accurately capture complex multiscale dynamics, even in high-dimensional dynamical systems.