Publication

Abstract : In summary, this study aims to bridge the gap between stochastic dynamics and neural excitable systems by introducing a novel methodology that combines Physics Informed Neural Networks with the stochastic FitzHugh–Nagumo equation. A standard model in biophysics and neuroscience, the FitzHugh–Nagumo (FHN) equation is used extensively to explain the dynamics of excitable systems, including cardiac tissues and brain membranes. In this study, we delve into the realm of stochasticity by exploring the stochastic FHN equation and its associated behaviors, focusing on both stability analysis and efficient numerical simulations. While traditional stability analysis techniques struggle with computational complexity, our hybrid approach combines PINNs with Euler–Maruyama for efficient numerical solutions with analytical methods for rigorous stability proofs in “Stability Analysis” section. Motivated by the need to overcome these limitations, we propose a novel approach that leverages Physics Informed Neural Networks (PINNs). By combining the expressive power of neural networks with the underlying physical principles governing the FHN equation, we develop a PINN-based solver that combines neural networks to approximate solutions, and a loss function derived from the Euler–Maruyama discretization of the stochastic FHN equation. This bypasses the need for mesh-based methods while preserving physical constraints. By doing so, we aspire to provide a deeper insight into the intricate interactions between deterministic and stochastic factors, advancing our ability to analyze, predict, and control the behavior of complex excitable systems in both biological and technological domains.