基于新工科背景下人工智能与偏微分方程交叉融合课程教学改革的研究与实践

Research and Practice on the Teaching Reform of the Cross Integration Curriculum of Artificial Intelligence and Partial Differential Equations under the Background of New Engineering

摘要: 随着人工智能的快速发展，我们提出了“AI × PDE”课程改革方案，旨在解决传统课程中基础衔接不足、学科交叉缺失、实践薄弱等问题，构建“理论–方法–实践”三位一体的教学体系。改革内容聚焦优化基础课程，融入AI求解偏微分方程(PDE)的前沿技术，推动学科交叉，建立动态课程机制，实施多元化考核体系，将实验报告、专题讨论纳入评估(占比30%)，强化过程性评价。教学实践表明，该方案有效提升了学生的数理建模能力、编程实践水平与跨学科创新思维，通过PINNs方法复现与改进等环节，培养出具备AI与PDE深度融合能力的交叉学科人才。

Abstract: With the rapid development of artificial intelligence, we have proposed an “AI × PDE” curriculum reform plan. This plan aims to address issues in traditional courses such as insufficient foundational cohesion, lack of interdisciplinary integration, and weak practical components, thereby establishing a tripartite “theory-methodology-practice” teaching system. The reform focuses on optimizing foundational courses, incorporating cutting-edge AI techniques for solving partial differential equations (PDEs), promoting interdisciplinary collaboration, establishing a dynamic curriculum mechanism, and implementing a diversified assessment system. This system incorporates lab reports and thematic discussions (accounting for 30% of the grade) to strengthen process assessment. Teaching practice has demonstrated that this plan effectively enhances students’ capabilities in mathematical modeling, programming practice, and interdisciplinary innovative thinking. Through activities such as reproducing and improving Physics-Informed Neural Networks (PINNs), the program cultivates interdisciplinary talent equipped with deep integration capabilities in both AI and PDEs.