Neural network surrogates for action potentials.

Area of Science:

• Computational neuroscience
• Biophysics
• Machine learning

Background:

• Excitable dynamics, crucial for cardiac and neuronal function, are often modeled using systems like FitzHugh-Nagumo.
• Neural networks offer potential as surrogate models for these complex dynamical systems.

Purpose of the Study:

• To investigate and compare the efficacy of different neural network architectures for modeling excitable dynamics.
• To assess surrogate model performance based on stability, error accumulation, and fidelity to the underlying system.

Main Methods:

• Comparison of three neural network architectures: data-driven feedforward networks, physics-informed neural networks (PINNs), and recurrent neural networks (RNNs).
• Evaluation of models using the FitzHugh-Nagumo system, focusing on temporal evolution of action potentials.
• Assessment metrics included stability, long-horizon error, and qualitative/quantitative fidelity.

Main Results:

• Data-driven feedforward networks provide accurate, stable approximations in data-rich environments, enabling fast inference.
• Recurrent neural networks struggle with long-term stability, showing significant error growth.
• PINNs demonstrate utility in data-scarce settings by leveraging physics-based regularization to improve identifiability and reduce extrapolation errors.
• Parameter regimes near bifurcations present learning challenges, partially mitigated by physics-informed losses.

Conclusions:

• Neural network surrogates can accelerate simulations of excitable dynamics, achieving speedups over traditional solvers in simpler cases.
• While promising, classical differential-equation solvers remain more robust for complex, highly parameterized problems.
• The choice of architecture depends on data availability and the specific characteristics of the dynamical system being modeled.