Predicting the thermodynamics in the chromosphere from the translation of SDO data into the IRIS$^{2}$ inversion results using a visual transformer model

We present SDO2IRIS$^2$: a visual transformer model that translates a combination of images of the chromosphere and transition region (TR), observed by AIA, and a line-of-sight magnetogram, provided by HMI, into temperature, line-of-sight velocity (v$_{los}$), velocity of the turbulent motions (v$_{turb}$), and electron density (n$_{e}$) in the chromosphere. Using the thermodynamic variables obtained from the inversion of the chromospheric lines Mg II h&k, observed by IRIS, as the target of the model, and the intensity images in the chromosphere and TR, and the photospheric magnetogram as the input, the predicted T and n$_{e}$ show a strong correlation ($\approx 0.80$) for $\approx$80% of the test inverted data, a moderate-to-strong correlation ($\approx0.63$) for 70% of the v$_{turb}$ of the target test inverted data, while for the $v_{los}$, the correlation is weak. Therefore, the predicted values by SDO2IRIS$^2$ may be used as an estimation of the thermodynamics in the chromosphere, either as a stand-alone result or as complementary information to other chromospheric data observed simultaneously. The execution time employed by SDO2IRIS$^2$ to obtain the thermodynamic values in the chromosphere is of the order of a few minutes, being $\le10$ minutes when using a CPU, and $\le5$ minutes when using a GPU. SDO2IRIS$^2$ opens a new avenue for the use of SDO data thanks to the inversions provided by IRIS observables.