Neural network surrogates for action potentials

In this study, we investigate neural network surrogate models for excitable dynamics using the FitzHugh-Nagumo system as a canonical reduced model of cardiac and neuronal action potentials. We compare three classes of architectures-data-driven feedforward networks, physics-informed neural networks (PINNs), and recurrent neural networks (RNNs)-and assess their ability to reproduce the temporal evolution of action potentials. Our evaluation emphasizes stability, long-horizon error accumulation, and fidelity to both the qualitative and quantitative features of the underlying dynamical system. We find that purely data-driven feedforward surrogates can provide accurate and stable approximations in data-rich regimes, offering fast inference and direct access to the solution at arbitrary time points. In contrast, recurrent architectures exhibit substantial error growth over long time horizons, highlighting persistent challenges in learning stable excitable dynamics. PINNs are most beneficial in data-scarce settings, where physics-based regularization improves identifiability and reduces extrapolation error. We further show that parameter regimes near bifurcations are particularly difficult to learn; incorporating physics-informed loss terms can partially alleviate these failures, though not eliminate them. For simple configurations, the proposed surrogates achieve speedups of up to 1.7× over conventional numerical solvers while remaining fully differentiable. However, for more complex and highly parameterized problems, classical differential-equation solvers remain more robust and accurate than the neural surrogate approaches considered here.