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.

翻译：我们提出了一种结合分裂方法与物理信息神经网络（PINNs）的新方法，用于求解前向微分方程组。所提出的分裂PINN方法有效解决了将PINNs应用于前向动力系统时的挑战，并通过其在神经元模型中的应用展示了精度的提升。具体而言，我们采用算子分裂将原始神经元模型分解为若干子问题，随后利用PINNs分别求解。此外，针对分数阶神经元模型中的分数阶导数，我们开发了一种L¹离散格式，从而提高了精度与效率。本研究结果凸显了分裂PINN在求解整数阶与分数阶神经元模型，以及计算科学与工程中其他类似系统方面的潜力。