We introduce a new approach for solving forward systems of differential equations 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 improved accuracy through its application to neuron models. Specifically, we apply operator splitting to decompose the original neuron model into sub-problems that are then solved using PINNs. Moreover, we develop an $L^1$ scheme for discretizing fractional derivatives in fractional neuron models, leading to improved accuracy and efficiency. The results of this study highlight the potential of splitting PINNs in solving both integer- and fractional-order neuron models, as well as other similar systems in computational science and engineering.

本研究提出了一种新的方法，splitting PINN, 通过将物理信息神经网络（PINNs）与分裂方法相结合，成功地应用到前向动力系统中，改进了神经元模型的精度，并发展出了一个$L^1$方案来离散分数阶导数，在解决整数和分数阶神经元模型等方面具有潜在的优势。

基于物理知识的神经网络分裂方法推断整数和分数阶神经元模型的动力学