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Abstract A multilayer spectral inversion (MLSI) model has recently been proposed for inferring the physical parameters of plasmas in the solar chromosphere from strong absorption lines taken by the Fast Imaging Solar Spectrograph (FISS). We apply a deep neural network (DNN) technique in order to produce the MLSI outputs with reduced computational costs. We train the model using two absorption lines, H α and Ca ii 8542 Å, taken by FISS, and 13 physical parameters obtained from the application of MLSI to 49 raster scans (∼2,000,000 spectra). We use a fully connected network with skip connections and multi-branch architecture to avoid the problem of vanishing gradients and to improve the model’s performance. Our test shows that the DNN successfully reproduces the physical parameters for each line with high accuracy and a computing time of about 0.3–0.4 ms per line, which is about 250 times faster than the direct application of MLSI. We also confirm that the DNN reliably reproduces the temporal variations of the physical parameters generated by the MLSI inversion. By taking advantage of the high performance of the DNN, we plan to provide physical parameter maps for all the FISS observations, in order to understand the chromospheric plasma conditions in various solar features.