Relationship between green financial innovation development measurement and social economy based on BP algorithm

To analyze the development of green finance, the weights of each green finance indicator are determined by the entropy value method. To analyze the role mechanism of green financial development on economic growth and to get the relationship between the two more clearly, the study optimizes the parameters of BP network with genetic algorithm and constructs correlation analysis model. The scores of green financial development in some regions show that the development level of the Yangtze River Delta is the highest, with an average score of 62.4. The heavy industries in North China and Northeast China are well developed and have a greater demand for green financial products, with an increase of 12.7% and 11.9% respectively. The economic growth of the corresponding regions shows that the economic development level of Chang San is higher and that of the Northeast is lower. The results of the GA-BP model training show that the convergence of the algorithm is fast and the curve increases rather than decreases in the validation set, indicating that the model is well trained and the error has reached the minimum value. The mean square error of the correlation analysis model is below 0.02 and the fit coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> is above 0.85, indicating the high accuracy of the results and the superior fit. The empirical evidence finds that the higher the level of green finance development, the better its economic development, and after a certain peak, the promotion effect diminishes. At present, some regions need to increase the proportion of green financial industries and accelerate industrial restructuring to achieve a green economy.