This article investigates the uniqueness of the solution for the conjugation problem of third-order PDE with a characteristic line and its application in neural network regularization. A theorem on the uniqueness of the solution for the considered class of equations is proven. Based on the obtained theoretical results, a novel neural network regularization method is developed that accounts for the physical constraints of the problem. A comparison is made between the classical finite difference method and an innovative approach based on physics-informed neural networks. Numerical experiments demonstrated that the proposed method provides higher accuracy and better adherence to the physical constraints of the problem. The regularized neural networks exhibited lower mean square error, better compliance with conjugation conditions, and higher resilience to input data variations compared to classical methods and standard neural networks. The research opens new perspectives for integrating classical mathematical methods with modern machine learning technologies.