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Neural network solvers represent an innovative and promising approach fortackling time-fractional partial differential equations by utilizing deeplearning techniques. L1 interpolation approximation serves as the standardmethod for addressing time-fractional derivatives within neural networksolvers. However, we have discovered that neural network solvers based on L1interpolation approximation are unable to fully exploit the benefits of neuralnetworks, and the accuracy of these models is constrained to interpolationerrors. 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 fractionalderivatives using Hermite interpolation techniques, and rigorously analyze itsapproximation accuracy. Afterward, taking into account the infinitelydifferentiable properties of deep neural networks, we integrate the high-orderHermite interpolation explicit approximation scheme with deep neural networksto propose the HNS. The experimental results show that HNS achieves higheraccuracy than methods based on the L1 scheme for both forward and inverseproblems, as well as in high-dimensional scenarios. This indicates that HNS hassignificantly improved accuracy and flexibility compared to existing L1-basedmethods, and has overcome the limitations of explicit finite differenceapproximation methods that are often constrained to function valueinterpolation. As a result, the HNS is not a simple combination of numericalcomputing methods and neural networks, but rather achieves a complementary andmutually reinforcing advantages of both approaches. The data and code can befound at \url{https://github.com/hsbhc/HNS}.

HNS: An Efficient Hermite Neural Solver for Solving Time-Fractional Partial Differential Equations