Quasars have long been known as intrinsically variable sources, but the physical mechanism underlying the temporal optical/UV variability is still not well understood. We propose a novel nonparametric method for modeling and forecasting the optical variability of quasars utilizing an autoencoder neural network to gain insight into the underlying processes. The autoencoder is trained with ~15,000 decade-long quasar light curves obtained by the Catalina Real-time Transient Survey selected with negligible flux contamination from the host galaxy. The autoencoder’s performance in forecasting the temporal flux variation of quasars is superior to that of the damped random walk process. We find a temporal asymmetry in the optical variability and a novel relation - the amplitude of the variability asymmetry decreases as luminosity and/or black hole mass increases - is suggested with the help of autoencoded features. The characteristics of the variability asymmetry are in agreement with those from the self-organized disk instability model, which predicts that the magnitude of the variability asymmetry decreases as the ratio of the diffusion mass to inflow mass in the accretion disk increases.