The National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST) will provide high-resolution, multi-line spectropolarimetric observations that are poised to revolutionize our understanding of the Sun. Given the massive data volume, novel inference techniques are required to unlock its full potential. Here, we provide an overview of our "SPIn4D" project, which aims to develop deep convolutional neural networks (CNNs) for estimating the physical properties of the solar photosphere based on DKIST observations. We describe the magnetohydrodynamic (MHD) modeling and the Stokes profile synthesis pipeline that produce the simulated output and input data, respectively. These data will be used to train a set of CNNs that can rapidly infer the 4D MHD state vectors by exploiting the spatiotemporally coherent patterns in the Stokes-profile time series. Specifically, our radiative MHD model simulates the small-scale dynamo actions that are prevalent in quiet-Sun and plage regions. Four cases with different mean vertical magnetic fields have been conducted; each case covers six solar-hours, totaling 64 TB in data volume. The simulation domain covers 25x25x8 Mm with 16x16x12 km spatial resolution, extending from the upper convection zone up to the temperature minimum. The outputs are generated at a 40 s cadence. We forward model the Stokes profile of two sets of Fe1 lines at 630 and 1565 nm, which will be simultaneously observed by DKIST and can better constrain the parameter variations along the line of sight. The MHD model output and the synthetic Stokes profiles are publicly available.
