用表征复杂化学反应系的平衡态或宏观化学动力学的无量纲数群张成多维空间，以处理材料制备或工业生产优化工作中的数据，结果表明：优化区和作业区的拓扑关系有4种类型．采用包括逆映照和未探优化区搜索方法、超平面识别法在内的模式识别、人工神经网络、遗传算法程序总结数学模型和优化策略．由这些程序组成的KDPAG专家系统应用于化工、石油化工和冶金等生产优化，材料优化设计，取得良好效果。 The multi-dimensional space is expanded into a multi-dimensional space by using the non-dimensional group of numbers that characterize the complex chemical reactions or the macroscopic chemical kinetics. The results show that the topological relations between the optimization area and the work area are 4 Kind of type Mathematical models and optimization strategies are summarized using pattern recognition, artificial neural networks, and genetic algorithm programs including inverse mapping and unexplored area search methods and hyperplane recognition methods. The KDPAG expert system composed of these programs is applied to the production optimization, material optimization and design of the chemical industry, petrochemical industry and metallurgy, and achieved good results.