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The higher education system is the driving force of social development, and the level of higher education is an important factor to judge whether a country is strong or not. In the process of promoting the popularization of higher education, the directions and policies of different countries are different. In order to evaluate the health and sustainability of each country's higher education system, this research has established an evaluation model based on BP neural network and gray model. First, we collected data on 10 indicators on higher education in six countries over the past decades, divided into two categories: national higher education investment and national higher education achievement. Then, we use the main component analysis method to reduce the dimensional processing of the data to solve the problem that too much data causes the model to converge too slowly. Second, we have established a national higher education health evaluation model based on BP neural network. Then we optimize BP neural network by PSO, which improves the speed and stability of the evaluation model. We get the six countries' higher education health ratings which are United States V, Germany III, Japan IV, Australia II, South Africa I and India I. Third, we have established a national sustainability evaluation model for higher education based on the grayscale model. We translate sustainability into a national higher education rating that predicts the future, and a high rating in the future means a strong sustainability. The final six countries to obtain the higher education health ratings are United States V, Germany III, Japan IV, Australia II, South Africa I and India II. By evaluating the health and sustainability of a country's higher education, we can give corresponding suggestions and policy support for the country to improve the level of higher education.

Health and Sustainability of National Higher Education Evaluation Model Based on BP Neural Network and Grey Model