Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for addressing time-fractional derivatives within neural network solvers. However, we have discovered that neural network solvers based on L1 interpolation approximation are unable to fully exploit the benefits of neural networks, and the accuracy of these models is constrained to interpolation errors. In this paper, we present the high-precision Hermite Neural Solver (HNS) for solving time-fractional partial differential equations. Specifically, we first construct a high-order explicit approximation scheme for fractional derivatives using Hermite interpolation techniques, and rigorously analyze its approximation accuracy. Afterward, taking into account the infinitely differentiable properties of deep neural networks, we integrate the high-order Hermite interpolation explicit approximation scheme with deep neural networks to propose the HNS. The experimental results show that HNS achieves higher accuracy than methods based on the L1 scheme for both forward and inverse problems, as well as in high-dimensional scenarios. This indicates that HNS has significantly improved accuracy and flexibility compared to existing L1-based methods, and has overcome the limitations of explicit finite difference approximation methods that are often constrained to function value interpolation. As a result, the HNS is not a simple combination of numerical computing methods and neural networks, but rather achieves a complementary and mutually reinforcing advantages of both approaches. The data and code can be found at \url{https://github.com/hsbhc/HNS}.

翻译：神经求解器通过利用深度学习技术，为解决时间分数阶偏微分方程提供了一种创新且前景广阔的方法。L1插值近似是神经求解器中处理时间分数阶导数的标准方法。然而，我们发现基于L1插值近似的神经求解器无法充分利用神经网络的优势，且这些模型的精度受限于插值误差。本文提出了一种高精度埃尔米特神经求解器（HNS），用于求解时间分数阶偏微分方程。具体地，我们首先利用埃尔米特插值技术构建了分数阶导数的高阶显式逼近格式，并严格分析了其逼近精度。随后，考虑到深度神经网络无限可微的性质，我们将高阶埃尔米特插值显式逼近格式与深度神经网络相结合，提出了HNS。实验结果表明，在正向问题、逆向问题以及高维场景下，HNS均比基于L1格式的方法实现了更高的精度。这表明，与现有基于L1的方法相比，HNS在精度和灵活性上均有显著提升，并克服了显式有限差分逼近方法常局限于函数值插值的局限性。因此，HNS并非数值计算方法与神经网络的简单组合，而是实现了两者优势互补与相互增强。数据和代码可在\url{https://github.com/hsbhc/HNS}获取。