Systematic modeling of the aging trend and the impact of silver economy in China

As China rapidly transitions into a deeply aging society, the repercussions of aging on economic growth and social security systems are intensifying. This study develops a multi-module modeling framework integrating deep learning, Bayesian inference, regularization regression, and coupled differential systems to assess aging’s macroeconomic and pension system impacts. Utilizing a Long Short-Term Memory neural network, we predict the proportion of those aged 65+ will surpass 19% by 2035. A happiness index for the elderly, constructed from China Health and Retirement Longitudinal Study data, highlights mental health, life satisfaction, and physical condition as key positive drivers, with notable regional variations. Elastic Net regression reveals that elderly consumption, pension participation, and service supply significantly boost gross domestic product. A coupled differential equation system indicates pension expenditure growth outpaces income, potentially creating a trillion-yuan gap by 2035, threatening system sustainability.