FLAME: Fitting Ly$\alpha$ Absorption lines using Machine learning

We introduce FLAME, a machine-learning algorithm designed to fit Voigt profiles to HI Lyman-alpha (Ly$\alpha$) absorption lines using deep convolutional neural networks. FLAME integrates two algorithms: the first determines the number of components required to fit Ly$\alpha$ absorption lines, and the second calculates the Doppler parameter $b$, the HI column density N$_{\rm HI}$, and the velocity separation of individual components. For the current version of FLAME, we trained it on low-redshift Ly$\alpha$ forests observed with the far-ultraviolet gratings of the Cosmic Origin Spectrograph (COS) on board the Hubble Space Telescope (HST). Using these data, we trained FLAME on $\sim$ $10^6$ simulated Voigt profiles which we forward-modeled to mimic Ly$\alpha$ absorption lines observed with HST-COS in order to classify lines as either single or double components and then determine Voigt profile-fitting parameters. FLAME shows impressive accuracy on the simulated data, identifying more than 98\% (90\%) of single (double) component lines. It determines $b$ values within $\approx \pm{8}~(15)$ km s$^{-1}$ and log $N_{\rm HI}/ {\rm cm}^2$ values within $\approx \pm 0.3~(0.8)$ for 90\% of the single (double) component lines. However, when applied to real data, FLAME's component classification accuracy drops by $\sim$ 10\%. Nevertheless, there is reasonable agreement between the $b$ and N$_{\rm HI}$ distributions obtained from traditional Voigt profile-fitting methods and FLAME's predictions. Our mock HST-COS data analysis, designed to emulate real data parameters, demonstrates that FLAME is able to achieve consistent accuracy comparable to its performance with simulated data. This finding suggests that the drop in FLAME's accuracy when used on real data primarily arises from the difficulty in replicating the full complexity of real data in the training sample.