<p>In recent years, neural-network-based methods have emerged as powerful tools for solving partial differential equations. Physics-Informed Neural Networks (PINNs) and Deep Neural Networks (DNNs) have demonstrated certain capabilities in dealing with such problems. However, these traditional methods often struggle to fully utilize the unique mathematical properties of the equations. Typically, they rely on approximations obtained through training to find solutions. In contrast, the bilinear neural network method and neural network-based symbolic calculation approach combine the advantages of neural network models with bilinear forms or original equations, and obtain exact solutions through symbolic computation and mathematical reasoning. In this paper, the bilinear neural network method and the neural network-based symbolic calculation approach are applied to the (3+1)-dimensional Kairat-X extended equation. As a result, exact solutions can be obtained directly, instead of being approximated through a training process. Moreover, new activation functions are innovatively used in this process. The introduction of new activation functions enhances the model’s capability to capture a broader range of solutions, which is crucial for exploring the solution space structure of complex (3+1)-dimensional Kairat-X extended equation. The obtained exact solutions provide new physical insights into the properties of the (3+1)-dimensional Kairat-X extended equation and show potential application prospects in fields such as fluid mechanics, nonlinear optics, and plasma physics.</p>