Numerical approaches have played a pivotal role in understanding and predicting the behavior of Landau phase transition materials for decades. However, the complexity of energy minimization techniques presents a significant challenge to their broader application. To address this barrier, we propose the Physics-Informed Neural Network (PINN) framework as a robust yet straightforward tool for solving physical problems, specifically for predicting the relaxed states of Landau phase transition materials. We introduce Action-PINN, a PINN designed to directly minimize the action functional, inspired by the variational principle. This approach incorporates changes in the loss function and architectural modifications, such as residual blocks and short connections, to mitigate issues like the high sensitivity of automatic differentiation near phase boundaries. These enhancements stabilize training, enabling the model to bypass explicit temporal dynamics and efficiently identify globally relaxed points. By applying Action-PINN to various Landau phase transition problems, we demonstrate its generality and accuracy in predicting globally relaxed states. A comparison with a numerical result demonstrates that Action-PINN offers advantages in effectively enhancing fidelity through transfer learning.