Determination of Linear Force- Free Magnetic Field Constant αα Using Deep Learning Bernard Benson, Zhuocheng Jiang, W. David Pan Dept. of Electrical and Computer Engineering (Dept. of ECE) G. Allen Gary and Qiang Hu Center for Space Plasma and Aeronomic Research (CSPAR) University of Alabama in Huntsville (UAH) Huntsville, Alabama 35899
Outline Research Background and Motivation Problem Statement Linear Force-Free Magnetic Fields (LFFF) Coronal Loops and Double Dipole Configuration Construction of Image Datasets of Coronal Loops Deep Learning Algorithms and Computational Platforms Simulation Results Conclusions Acknowledgement
Magnetic Field of the Sun The Sun is a magnetically driven star. The magnetic field of the Sun is dominant over other forces in the solar corona. Part of free magnetic energy in solar corona is released during solar activity. The magnetic energy can be calculated by obtaining an accurate magnetic field model for an active region. Image courtesy of NASA SDO: AIA http://aia.lmsal.com/index.html
Solar Magnetic Activity Impact on Earth Large coronal eruptions like flares and coronal mass ejections can influence Earth s magnetic field. This may trigger magnetic storms. Coronal eruptions also can cause harmful effects: - Disturbances in communications - Damages to satellites - Causing power outages - Causing life-threatening radiation damage to astronauts in space Image courtesy of http://sohowww.nascom.nasa.gov/gallery/images/magnetic clean.html.
Magnetograms Reliable high accuracy magnetic field measurements are only available in the photosphere (the visible surface of the Sun we are familiar with). These measurements are called vector magnetograms. They provide the magnetic field vector in the photosphere. NASA SDO/AIA 171 Angstroms image and potential field line (Oct. 25, 2010)
Research Objectives It is important to determine a high-fidelity magnetic model to understand and predict the dynamics in the corona. As the first step, we used the simplest model with one parameter that is indicative of the non-potential nature of an active region. The model allows us to generate a set of pseudo-coronal loop images, which can be used to derive the model parameter αα. Deep learning algorithms would be applicable due to the difficulty of determining the appropriate image features for pattern classification -- choosing the best αα value from a set of admissible values. To the best of our knowledge, this would be the first attempt to use artificial intelligence to estimate the solar magnetic model parameter directly from pseudo-coronal loop images.
Filtergram: A photograph of the sun at a particular frequency range (by means of a variable filter). Problem Statement To investigate the feasibility and effectiveness of Deep Learning Algorithms to solve for magnetic field parameter (αα) using digital images of synthesized EUV (Extreme Ultraviolet) coronal filtergrams. Terminology:
Linear Force-Free Magnetic Fields The solar magnetic field above the photosphere has been modeled by using force-free fields (FFF). The fields have been employed since they are the simplest field which are non-potential. Linear force-free fields are characterized by BB = αα BB and. BB = 0 Where B is the magnetic induction field and the force-free parameter αα is a constant.
Coronal Loops Simple coronal loops are modelled by using two nearby foot points which represents the outer surface of a coronal loops. These two field lines are projected to the z = 0 surface. The two field lines are made into a polygon and filled. We use 150 such foot points to generate our datasets within a 40 40 40 box. The value of αα corresponds to the variation of twists in the loops.
LFFF Double Dipole Configuration Negative Dipole Positive Dipole PPPPPPPPPPPPPPPPPPPP: NN xx = NN yy = NN zz = 40, αα = 0.05, dd zz = 5.0, xx oo = 0, yy oo = 20, 150 rrrrrrrrrrrr ffffffff pppppppppppp
Image Datasets of Coronal Loops Stationary Dipole Loops with 1000 images per class of αα
Datasets of Coronal Loops Images Varying Dipole Loops with 5000 images per αα
Deep Learning Algorithms Classify input images into one out of 11 possible αα values. We experimented with the well-known deep learning algorithms: LeNet-5 (about 18 million parameters) AlexNet (about 28 million parameters) Sparse Autoencoders (to extract features automatically) We divided our datasets into: - Training (70%) - Validation (15%) - Testing (15%)
LeNet-5 Convolutional Neural Network Architecture C1: feature maps 20 116 116 S2: f. maps 20 58 58 C3: f. maps 50 54 54 S4: f. maps 50 27 27 C5: layer 500 F6: layer 500 OUTPUT 11 INPUT 120 120 Full connection Gaussian connections Full connection Convolutions Subsampling Convolutions Subsampling
Figure copyright Alex Krizhevsky, Ilya Sutskever, and Geoffrey Hinton, 2012 AlexNet Convolutional Neural Network Architecture CONV1 MAX POOL1 NORM1 CONV2 MAX POOL2 NORM2 CONV3 CONV4 CONV5 Max POOL3 FC6 FC7 FC8 11 ReLU (Rectified Linear Unit) activation function reduces compute time compared to sigmoid or tanh activations in LeNet-5. Dropout to avoid overfitting. Training occurs over 30 epochs.
Sparse Autoencoders Training occurs in an unsupervised manner using training images of size 50 50. Two sparse autoencoders used with 100 and 50 hidden units, respectively. Softmax activation was used for classification.
Simulation Results: Validation Accuracy and Loss
Computational Platform and Efficiencies Computational Platform: Deep Learning DevBox with 4 NVIDIA Titan X GPUs, running Nvidia DIGITS software. Training Times - 2 mins for LetNet-5, 5 mins for AlexNet Testing Times - 8 seconds for LetNet-5, 10 seconds for AlexNet
Simulation Results Very high accuracy using AlexNet on both datasets. Top-1 accuracy: 99.6% and 96.4% Top-5 accuracy: 100% Reduced top-1 accuracy (85.49%) on varying dipole dataset due to the absence of dropout in LeNet-5, Top-5 accuracy of 99.88%. High sensitivity, specificity and precision show results are not skewed to uneven test cases.
Confusion Matrix Confusion matrix varying dipole loops dataset using 750 images per class of αα. High accuracy demonstrated per each class. Accurate within top-3 guesses.
Conclusions We have shown that given sufficient training data deep learning methods can find the magnetic field parameter αα from a set of pseudo-coronal loop images. The challenge is being able to generate high fidelity coronal loop images to test our models on observed EUV filtergrams. We are currently generating more complex coronal loop images using multiple dipole configurations and testing them on deep learning frameworks. As more data are being generated by NASA s SDO mission, sufficient data are available to extract features from AIA (Atmospheric Imaging Assembly) and HMI (Helioseismic and Magnetic Imager) images.
Acknowledgement We want to thank the support from the Cross College Faculty Research (CCFR) Program sponsored by The University of Alabama in Huntsville (UAH).