Research On Addition Of Auxiliary Quantities To Plane Geometry Problems Based On Graph Neural Network

In contemporary times,the scope of application of artificial intelligence is no longer limited to the fields of natural language processing,speech recognition,and computer vision.With its excellent learning capabilities and responsiveness,human society can tackle a wide range of complex problems.Human-like problem solving is one of the most popular fields of research in artificial intelligence,which aims to solve mathematical problems automatically by using computer programs.The machine proof of the planar geometry theorem based on mathematical logic has met with great success.However,the existing proof engine does not simulate human geometric intuition very well.It replaces the human to complete the addition of auxiliary quantities,which is an important problem that the machinery of the plane geometry theorem has not solved for a long time.In the development and maturation of graph neural network,new ideas are provided for adding auxiliary quantities.Therefore,this thesis researches the addition of planar geometric auxiliary quantity based on graph neural network,and designs and implements a planar geometric auxiliary quantity addition method based on graph isomorphic network.The main contents of this paper include the following three sections:(1)Design of graphic representation method based on plane geometry.Firstly,the geometric knowledge is extracted from the topic by the relation extracting template.Then,the knowledge of plane geometry is defined as predicate representation and consists of two classes:entity and relational predicate.Finally,the entity predicates are converted to nodes,and the relational predicates are converted to adjacency matrices to generate graph data containing geometric element constraint information and numerical data.(2)Construction of densely labeled planar geometric datasets for graph neural training.First of all,many middle school mathematics textbooks are collected on the subject of plane geometry,the subject information,such as text,pictures,solution flow,ideas,etc.Then,use the attribute correlation the production rules are used to perform simple reasoning and expand the topic information.Finally,through data cleaning,the graph dataset can be used for geometric resource retrieval and training of graph neural network samples.(3)Design of planar geometric auxiliary quantity addition method based on graph isomorphic neural network.The existing methods of auxiliary quantity addition are analyzed and summarized.The data set and policy classification are used for graph isomorphic neural network training,and the decision network model with automatic addition of auxiliary quantities is obtained.Combined with the recommendation algorithm oriented by the target problem,the auxiliary quantity addition method based on graph neural network is finally realized.After testing 128 plane geometry problems that require auxiliary quantities,the results show that 61.7% of the problems can be solved after applying the auxiliary quantity addition strategy generated by this method.This verifies the good feasibility and effectiveness of the method.