This study forecasts the VKOSPI index, a key volatility indicator in the Korean stock market, using various machine learning methods and an extensive set of explanatory variables, including stock market fund flows and supply-demand trends. A novel Multi-Input LSTM model is proposed, demonstrating superior predictive accuracy over traditional models like HAR. The machine learning models generally outperform the HAR model, with linear models excelling in short-term forecasts and non-linear models in long-term forecasts. The Multi-Input LSTM model's structure, which sequentially integrates categorized explanatory variables, significantly enhances its predictive power, particularly with the inclusion of stock market-related variables. The study's findings, based on data from January 4, 2016, to March 31, 2023, underline the importance of these variables in accurately predicting market volatility.