Abstract: Solving the neutron diffusion equation is the key to reactor design and analysis. In engineering applications, the neutron diffusion equation is often characterized by multi-dimensionality and multi-energy groups. When using a physics-informed neural network (PINN) to solve the transient neutron diffusion equation, challenges such as large volumes of training data, long computing time and high computational resource consumption may be encountered. To address these challenges, a PINN based on the Runge-Kutta method (PINN_RK) for solving the reactor neutron diffusion equation was introduced in this paper. The innovation of this paper is to integrate the high-order Runge-Kutta method into the traditional PINN framework, so that discretizes the temporal term in the neutron diffusion equation, thereby transforming the original transient problem into a sequence of steady-state problems at discrete time steps, and applying it to the solution of the high-dimensional neutron diffusion equation. This method reduces the amount of training data required and reduces the consumption of computing resources. As an illustration, in the two-dimensional neutron diffusion equation, the amount of transient data increased by two additional datasets compared with the amount of steady-state data. The sensitivity analysis on key parameters of the step size and order of the Runge-Kutta method was carried out by taking the two-dimensional slab reactor as an example of the neutron diffusion equation, which effectively balanced the accuracy and computational efficiency. Finally, by solving the one-dimensional, two-dimensional and three-dimensional slab reactor neutron diffusion equations, the method was preliminarily verified to be accurate and applicable to solving the high-dimensional neutron diffusion equations under the condition of using the optimal parameters of Runge-Kutta method. The experimental results show that in the one-dimensional slab reactor experiment, the PINN_RK numerical solution is highly consistent with the analytical solution. In the two-dimensional slab reactor experiment, the numerical solution of the model is highly consistent with the traditional numerical solution at different times, and the relative error is mainly concentrated near the boundary, and the mean square error at different times is less than 10⁻⁶. In the three-dimensional slab reactor experiment, the accuracy of the model numerical solution is slightly reduced, but the relative error is still low (about 6%). In general, in response to the problems of large data volume, long computing time and high resource consumption faced by PINN in solving high-dimensional neutron diffusion equations, the PINN_RK method significantly reduces the required training data volume and computing resource consumption by introducing the Runge-Kutta method. In the PINN_RK method, the data volume is reduced by two sets of numbers. At the same time, the high consistency between the PINN_RK numerical solution and the traditional numerical solution also proves that PINN_RK has significant potential and advantages in dealing with high-dimensional neutron diffusion equations in reactors.