Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models (Communications in Computational Physics, 2024)
We introduce a new approach for solving forward systems of differentialequations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the challenge of applying PINNs to forward dynamical systems and demonstrates improvedaccuracy through its application to neuron models. Specifically, we apply operatorsplitting to decompose the original neuron model into sub-problems that are thensolved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractionalderivatives in fractional neuron models, leading to improved accuracy and efficiency.The results of this study highlight the potential of splitting PINNs in solving bothinteger- and fractional-order neuron models, as well as other similar systems in computational science and engineering.
Keywords: Operator splitting; neuron models; fractional calculus.