Gaussian Graphical Models for Active Region Modeling and Flare Prediction

• Activity Number: 382 - Statistical and Machine Learning Efforts on Solar Flare Predictions II
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Yu Wang* and Alfred O. Hero, III
• Companies: University of Michigan and University of Michigan
• Keywords: Graphical models; Tensor-variate data; Solar flare prediction; Space physics; Optimization; Spatio-temporal statistics

Abstract

We propose a new Gaussian graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly to a global optimum of its objective function. We demonstrate the scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data acquired by the SDO/HMI and SDO/AIA instruments, where the proposed model is able to forecast the solar atmosphere and classify active regions based on the intensities of the solar flares.