Neural translation for Stokes inversion and synthesis

TL;DR

SENTIS addresses the computational bottleneck of Stokes-profile inversions by recasting the problem as neural machine translation between tokenized Stokes data and atmospheric stratifications. It uses a VQ-VAE to discretize both modalities and a transformer encoder–decoder to model the autoregressive posterior over atmospheric tokens given observed Stokes profiles, enabling fast inference and uncertainty quantification. Trained on a large synthetic dataset spanning $log tau500$ from -7.5 to 1.5 and including Fe I 630 nm and Ca II 854 nm with non-LTE considerations, the approach yields posteriors that are consistent with classical inversions and supports multi-line inversions with improved constraint in different atmospheric layers. Validation on Hinode SOT/SP data demonstrates comparable fidelity to traditional methods while offering orders-of-magnitude speed and posterior sampling capability for robust uncertainty assessment.

Abstract

[Abridged] The physical conditions in stellar atmospheres can be obtained from the interpretation of solar spectro-polarimetric observations. However, traditional inversion codes are computationally demanding, especially for lines whose formation is complex. The necessity of faster alternatives has motivated the emergence of machine learning solutions. This paper introduces an approach to the inversion and synthesis of Stokes profiles inspired by neural machine translation. Our aim is to develop a generative model that treats Stokes profiles and atmospheric models as two distinct ``languages'' encoding the same physical reality. We build a model that learns how to translate between them, also providing estimates of the uncertainty. We employ a tokenization strategy for both Stokes parameters and model atmospheres, which is learned using a VQ-VAE, a neural model used to compress the data into a lower dimensionality form. The core of our inversion code utilizes a transformer encoder-decoder architecture to perform the translation between these tokenized representations. The model is trained on a database of synthetic Stokes profiles derived from perturbations to various semi-empirical solar atmospheric models, ensuring a wide range of expected solar physical conditions. The method effectively reconstructs atmospheric models from observed Stokes profiles, showing better constrained models within the region of sensitivity of the considered spectral lines. The latent representation induced by the VQ-VAE helps accelerate the inversion by compressing the length of the Stokes profiles and model atmospheres. Additionally, it helps regularize the solution by reducing the chances of obtaining unphysical models. As a final advantage, the method provides the generative nature of our model, which naturally yields an estimate of the uncertainty in the solution.

Figures (9)

• Figure 1: Examples of the Stokes profiles (first two columns) and the model atmospheres (last three columns) used for training SENTIS. Solid lines represent the original data, while the dashed lines represent the reconstructed ones using the VQ-VAE model.
• Figure 2: VQ-VAE model used for tokenization. The encoder $\mathcal{E}$ produces a latent representation of the Stokes parameters and the model stratifications, which is then passed through the decoder $\mathcal{D}$ after quantization.
• Figure 3: Transformer encoder-decoder model. Both the encoder and decoder blocks are transformer layers..
• Figure 4: Samples from the generative model (orange curves) for the inversion of six Stokes profiles extracted from the test set. The blue curve is the original model, the green curve is the median model and the red curve is the greedy decoded model. The upper three rows show the results when the Fe i spectral region is used, the middle three rows show the results when the Ca ii spectral region is used, and the last three rows show the results when both spectral regions are used.
• Figure 5: Same of Fig. \ref{['fig:validation_inversion_thermo']} but for the magnetic field components.