Ramiz Qudsi
From state of caffeination to citation!
Algorithm Development for 3-D Magnetic Field topology Reconstruction Using Machine Learning
Ramiz A. Qudsi
Boston University
(qudsira@bu.edu)
(https://qudsiramiz.github.io)
https://slides.com/qudsi/imf_reconstruction
link to the presentation
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Multiscale nature of Interplanetary Magnetic Field (IMF)
Maruca 2021, Frontiers in A & SS
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Coleman (ApJ, 1968)
Bale et al. (Nature, 2019)
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Competing Theories of Turbulence
Critical effects of magnetic structure on plasma dynamics:
- Propagation of energetic particles
- 3D context of kinetic processes like magnetic reconnection
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How do we get the full 3D structure of magnetic field?
Put a magnetometer at every point in space
Launch a constellation of spacecraft with magnetometers on them
Compute values at rest of the points by interpolation
Conventional interpolation are not best suited
Gaussian Processes in Machine Learning
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Spacecraft configurations
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Some relevant scales:
d_i \mathrm{(1AU)} \sim 70 ~\mathrm{km} \\
V_{sw} \sim 500 ~\mathrm{km/sec} \\
X_{sim} \mathrm{(box size)} \sim 40 d_i\\
\hspace{3.1cm}\sim 4\times 10^3 \mathrm{km}\\
d_{spc} \sim [1, 22]~d_i\\
\hspace{1.2cm}\sim \mathrm{ [10^2, 10^3]~ km} \\
f[min,max] \sim V_{sw}/(2\times d_{spc, max, min}) \\
\hspace{0.8cm}\sim [0.25, 2.5]~\mathrm{Hz}\\
\nu (\mathrm{sampling~rate}) \sim 15 \mathrm{Hz}\\
\mathrm{(just~because~of~box~size~and~stuff)}\\
\mathrm{time~to~move~across~the~simulation~box} \sim 10 ~\mathrm{sec}
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Gaussian Process Regression Interpolation
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Gaussian Process Regression:
$$m(\mathbf{x}) = \mathbb{E}[f(\mathbf{x})]$$
Mean function
$$k(\mathbf{x}, \mathbf{x'}) = \mathbb{E}[(f(\mathbf{x}) - m(\mathbf{x}))(f(\mathbf{x'}) - m(\mathbf{x'}))]$$
Covariance function
$$f(\mathbf{x}) \sim \mathcal{GP}\left(m(\mathbf{x}), k(\mathbf{x}, \mathbf{x'})\right)$$
Gaussian Processes
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Constant
Linear
RBF
Matern
Kernels
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Results
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Reconstructed Magnetic field
Maruca 2021, Frontiers in A & SS
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Maruca 2021, Frontiers in A & SS
All components at a time
Qudsi et. al., in prep
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Single component input
Vector input
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Different configurations
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Errors in reconstruction
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\epsilon_{\rm B-*} = \frac{|\textbf{B}_{\rm sim}|- |\textbf{B}_{\rm rec}|}{|\textbf{B}_{\rm sim}|}
Error in magnetic field magnitude:
cos (\theta) = \frac{\textbf{B}_{\rm sim} \cdot \textbf{B}_{\rm rec}}{|\textbf{B}_{\rm sim}| |\textbf{B}_{\rm rec}|}
Error in magnetic field direction:
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Moving Forward
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What's next?
Explore the impact of relative spacecraft separation and arrangement
Incorporate the zero divergence condition on magnetic field
Explore alternative algorithms/methods
Deep Gaussian Processes
Neural Network as GP
Find better ways to compare the reconstructed images for different styles
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Thank You!
link to the presentation
slides.com/qudsi/imf_reconstruction
Thank You!
link to the presentation
Qudsi BU qudsira@bu.edu
slides.com/qudsi/imf_reconstruction
Reconstruction_BU
By Ramiz Qudsi
Reconstruction_BU
Thesis presentation!
