Machine learning for reconstruction of polarity inversion lines from solar filaments

TL;DR

The paper tackles reconstructing solar magnetic polarity maps from historical filament observations by modeling a polarity field $f:\mathcal{S}\to[-1,1]$ with the polarity inversion line as the zero level set $\{\vec{r}: f(\vec{r})=0\}$. It introduces a physics-informed fully connected neural network in cylindrical projection, trained via a loss $\mathcal{L}(f)$ that enforces filament constraints and global polarity balance, optionally augmented with reference-point priors to yield $\mathcal{L}^\dagger(f)$. With dense reference points, reconstructions resemble McIntosh Archive targets and uncertainties are quantified by 100 independent realizations; performance degrades without priors, highlighting the role of auxiliary information. The approach offers a semi-automatic pathway to historical polarity maps and motivates semi-supervised extensions that fuse chromospheric and magnetic data for long-term solar magnetism studies.

Abstract

Solar filaments are well-known tracers of polarity inversion lines that separate two opposite magnetic polarities on the solar photosphere. Because observations of filaments began long before the systematic observations of solar magnetic fields, historical filament catalogs can facilitate the reconstruction of magnetic polarity maps at times when direct magnetic observations were not yet available. In practice, this reconstruction is often ambiguous and typically performed manually. We propose an automatic approach based on a machine-learning model that generates a variety of magnetic polarity maps consistent with filament observations. To evaluate the model and discuss the results we use the catalog of solar filaments and polarity maps compiled by McIntosh. We realize that the process of manual compilation of polarity maps includes not only information on filaments, but also a large amount of prior information, which is difficult to formalize. In order to compensate for the lack of prior knowledge for the machine-learning model, we provide it with polarity information at several reference points. We demonstrate that this process, which can be considered as the user-guided reconstruction or super-resolution, leads to polarity maps that are reasonably close to hand-drawn ones, and additionally allows for uncertainty estimation.

Figures (14)

• Figure 1: Example of a synoptic map from McIntosh Archive.
• Figure 2: Projection of a synoptic map of solar filaments from 2D geometry (the left panel) onto cylinder $\mathcal{C} \subset \mathbb{R}^3$ (the right panel). The cylindrical projection contains a small gap between the edges of the image. This gap was introduced to account for the fact that there is no exact match between the left and right edges of the image, but only a similarity.
• Figure 3: Illustration of the function $f(\vec{r})$ defined on the plane of the synoptic map and approximating the polarity map. The orange color is for negative values of the function, the purple color is for positive values of the function. The green line is the zero-level of the function and is interpreted as the polarity inversion line.
• Figure 4: The architecture of the fully connected neural network applied for reconstruction of magnetic polarity maps. Circles represent neurons, lines show connections between neurons.
• Figure 5: Synoptic maps with auxiliary grids of reference points (green dots). The grid step, indicating the distance between adjacent green dots, is 32 pixels in image (a) and 64 pixels in image (b).