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We present a novel intelligent quasar continuum neural network (iQNet), predicting the intrinsic continuum of any quasar in the rest-frame wavelength range 1020 Angstroms $\leq λ\leq$ 1600 Angstroms. We train this network using high-resolution Hubble Space Telescope/Cosmic Origin Spectrograph ultraviolet quasar spectra at low redshift ($z \sim 0.2$) from the Hubble Spectroscopic Legacy Archive, and apply it to predict quasar continua from different astronomical surveys. We utilize the HSLA quasar spectra that are well-defined in the rest-frame wavelength range [1020, 1600] Angstroms with an overall median signal-to-noise ratio of at least five. The iQNet achieves a median AFFE of 2.24% on the training quasar spectra, and 4.17% on the testing quasar spectra. We apply iQNet and predict the continua of $\sim$3200 SDSS-DR16 quasar spectra at higher redshift ($2< z \leq 5$) and measure the redshift evolution of mean transmitted flux ($< F >$) in the Ly-$α$ forest region. We measure a gradual evolution of $< F >$ with redshift, which we characterize as a power-law fit to the effective optical depth of the Ly-$α$ forest. Our measurements are broadly consistent with other estimates of $<F>$ in the literature, but provide a more accurate measurement as we are directly measuring the quasar continuum where there is minimum contamination from the Ly-$α$ forest. This work proves that the deep learning iQNet model can predict the quasar continuum with high accuracy and shows the viability of such methods for quasar continuum prediction.