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In the new normal period, the trend changes and adjustments of the environment such as international trade, production capacity, labor supply and resource constraints have put forward new requirements for China's industrial development, which have brought new challenges and given new opportunities. In the new normal stage where economic growth continues to decline, industrial growth is still an important support for economic growth. The advancement of industrial technology is the main driving force for improving the total factor productivity of the industrial industry. Therefore, the most important thing to promote industrial growth is to upgrade the level of industrial technology. In response to the above-mentioned problems, this paper analyzed the relationship between industrial technology and industrial output in the new normal environment by using the BP neural network (BPNN) algorithm. The connection between the two has been found, which provided a clear direction for the functional adjustment of economic law. Experimental studies have shown that there is a positive relationship between industrial technological progress and industrial output. When other conditions are the same, and when the non-new normal is selected, industrial output increases by about 0.36% for every 1% increase in industrial technological progress. When choosing to be in the new normal, industrial technological progress has a higher impact on industrial output. For every 1% increase in technological progress, industrial output increases by about 0.39%. [ABSTRACT FROM AUTHOR]