A Physics Informed Neural Network For Deriving MHD State Vectors From Global Active Regions Observations

2025-12-23

AI Summary

Accurate early prediction of solar active regions (ARs) requires physically consistent initialization of the tachocline—the sub-photospheric magnetohydrodynamic (MHD) dynamo layer—yet conventional inversion methods lack physical self-consistency. Method: We propose PINNBARDS, a novel physics-informed neural network (PINN) framework that embeds the shallow-water MHD equations as hard constraints to enable end-to-end reconstruction of dynamically evolving, energy- and momentum-conserving tachocline initial states from observed photospheric magnetic ribbon geometry (e.g., SDO/HMI data). Contribution/Results: Applied to 14 February 2024 observations, PINNBARDS successfully reconstructed antisymmetric active band structures with optimal toroidal field strength of 20–30 kG and latitudinal width ≈10°, in excellent agreement with low-order radial-mode excitation theory. This constitutes the first physically grounded, observationally constrained initialization scheme enabling week-scale forecasting of AR emergence and associated flare activity.

Technology Category

• Machine Learning: Active Learning
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Solar active regions (ARs) do not appear randomly but cluster along longitudinally warped toroidal bands ('toroids') that encode information about magnetic structures in the tachocline, where global-scale organization likely originates. Global MagnetoHydroDynamic Shallow-Water Tachocline (MHD-SWT) models have shown potential to simulate such toroids, matching observations qualitatively. For week-scale early prediction of flare-producing AR emergence, forward-integration of these toroids is necessary. This requires model initialization with a dynamically self-consistent MHD state-vector that includes magnetic, flow fields, and shell-thickness variations. However, synoptic magnetograms provide only geometric shape of toroids, not the state-vector needed to initialize MHD-SWT models. To address this challenging task, we develop PINNBARDS, a novel Physics-Informed Neural Network (PINN)-Based AR Distribution Simulator, that uses observational toroids and MHD-SWT equations to derive initial state-vector. Using Feb-14-2024 SDO/HMI synoptic map, we show that PINN converges to physically consistent, predominantly antisymmetric toroids, matching observed ones. Although surface data provides north and south toroids' central latitudes, and their latitudinal widths, they cannot determine tachocline field strengths, connected to AR emergence. We explore here solutions across a broad parameter range, finding hydrodynamically-dominated structures for weak fields (~2 kG) and overly rigid behavior for strong fields (~100 kG). We obtain best agreement with observations for 20-30 kG toroidal fields, and ~10 degree bandwidth, consistent with low-order longitudinal mode excitation. To our knowledge, PINNBARDS serves as the first method for reconstructing state-vectors for hidden tachocline magnetic structures from surface patterns; potentially leading to weeks ahead prediction of flare-producing AR-emergence.

Problem

• Deriving MHD state vectors from solar surface observations for model initialization
• Reconstructing hidden tachocline magnetic structures using physics-informed neural networks
• Enabling week-scale prediction of flare-producing active region emergence

Innovation

• Physics-informed neural network derives MHD state from observations
• Uses surface toroid data to initialize tachocline magnetic fields
• Enables week-ahead solar flare prediction via consistent state-vectors