Nonlinear Adaptive Optimization of Multi-Modal Learning Paths Using Graph Convolutional Networks and Reinforcement Learning for Intelligent Educational Systems

Abstract This study proposes an adaptive multi-modal learning path optimization system based on Graph Convolutional Networks (GCN), attention mechanisms, and reinforcement learning to address the challenges faced by traditional recommendation methods in educational scenarios, including multi-modal data integration, temporal behavior modeling, and dynamic learning path optimization. The system constructs a user-resource interaction graph, incorporating knowledge point dependencies and temporal modeling to dynamically generate personalized learning paths. A multi-modal data fusion strategy is introduced, utilizing nonlinear mathematical modeling to dynamically adjust the weights of various learning resources—such as textbooks, videos, and coding exercises—according to different learning stages. Furthermore, Long Short-Term Memory (LSTM) networks and Transformer models are employed to capture the temporal dependencies of user learning behaviors, enhancing recommendation accuracy and user satisfaction. The reinforcement learning strategy optimizes recommendation objectives, significantly improving recommendation diversity and long-term learning outcomes. A case study on a "Computer Networks" course demonstrates the effectiveness of the system, showing substantial improvements in recommendation accuracy, diversity, and learning performance compared to traditional methods. By integrating mathematical modeling and nonlinear optimization techniques, this research offers an innovative technical approach for personalized learning recommendation systems in the field of intelligent education.