Comparing classical ordinary differential equation and neural network models for reduced-order single-cell electrophysiology

Abstract

Modeling cardiac electrophysiology plays a crucial role in advancing non-invasive diagnostics and enhancing our understanding of heart function. Historically, models describing excitable cells through systems of Ordinary Differential Equations (ODEs) have been the standard in electrophysiology modeling. These models range from detailed representations of ion channel dynamics to simplified reduced-order models that capture the behavior of excitability phenomenologically. In this work, we compare a fast reduced-order model with data-driven and physics-informed neural networks to assess their effectiveness as efficient replacements for numerical solutions. For this, the FitzHugh-Nagumo model was used, and scenarios with increasing complexity were studied. The networks were trained using numerical data and knowledge of model physics, derived from the ODEs. Additionally, several techniques were employed to improve training, including architecture optimization, increased point density in regions of high error, and time-domain splitting. Inference was conducted using the state-of-the-art TensorRT SDK to speed up model inference, leveraging tensor core matrix-matrix specialization to ensure maximum performance. We observed up to a 1.8x speedup compered to numerical models optimized and implemented in CUDA, with minimal loss in accuracy. These gains highlight valuable use cases for neural network emulators, as faster substitute for numerical methods when complexity can be controlled, while still emphasizing the prominence of equation-based modeling in cardiac electrophysiology in general due to their flexibility.