Spectropolarimetric Inversion in Four Dimensions with Deep Learning (SPIn4D): I. Overview, Magnetohydrodynamic Modeling, and Stokes Profile Synthesis

TL;DR

SPIn4D tackles the challenge of inferring the four-dimensional ($4$D) MHD state from DKIST's high-volume spectropolarimetric data by leveraging convolutional neural networks trained on radiative MHD simulations. The approach uses MURaM SSD simulations and forward-modeled Stokes profiles for Fe I lines at $630.15$ nm, $630.25$ nm, $1564.9$ nm, and $1565.2$ nm to generate training data, enabling CNNs to map Stokes time-series to 4D MHD state variables. The data set comprises six SSD cases totaling 109 TB, domains of at least $25\times25\times8$ Mm with $16\times16\times12$ km resolution, cadence $40$ s, and 13.7 TB in the initial public release. The work provides a foundation for rapid, 4D inferences, improving diagnostics of magnetic structure and energy transport in the photosphere and informing future inversion approaches for the DKIST era.

Abstract

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 from DKIST spectropolarimetric 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 four-dimensional 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. Six cases with different mean magnetic fields have been conducted; each case covers six solar-hours, totaling 109 TB in data volume. The simulation domain covers at least $25\times25\times8$ Mm with $16\times16\times12$ km spatial resolution, extending from the upper convection zone up to the temperature minimum region. The outputs are stored at a 40 s cadence. We forward model the Stokes profile of two sets of Fe I 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, with 13.7 TB in the initial release.

Figures (1)

• Figure 1: Schematic representation of the SPIn4D model workflow. The core of the model is the DL neural network, highlighted in blue in the middle of the diagram. The network Training step is outlined by the broken green line and uses data derived from the MURaM simulations, both the MHD variables themselves and the Stokes profiles $(I,Q,U,V)$ synthesized from the MHD data cubes (green lines). Once trained on the simulated data, Observed Stokes data can be input to the network (red arrow) to produce the most likely 3D MHD state as output (labeled "Predicted MHD Variables"). The network may be trained to receive single-time input Stokes data to produce a reduced dimensional output MHD state $(\boldsymbol{B}, v_z, P, T)$ or to receive multi-time input Stokes data to produce a full-dimensional MHD output, including additional Derived Outputs such as vector velocities, Poynting flux, and so on. The network may also be trained to produce the Derived Outputs directly.