Ramiz Qudsi
From state of caffeination to citation!
Gaussian Process Regression for Magnetic Field Reconstruction
https://slides.com/qudsi/magnetore
Some relevant scales:
d_i \mathrm{(1AU)} \sim 100 ~\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, 11]~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 40 \mathrm{Hz}\\
\mathrm{(just~because~of~box~size~and~stuff)}\\
\mathrm{time~to~move~across~the~simulation~box} \sim 10 ~\mathrm{sec}
Hub
Spacecrafts
$$d_i$$
22
Gaussian Process Regression Interpolation
Gaussian Process Regression:
It is a probabilistic data imputation method
It is a probability distribution over possible functions that fit the given finite dataset
dataset with finite number of observation is modelled as if it were a multivariate normal distribution
$$m(\mathbf{x}) = \mathbb{E}[f(\mathbf{x})]$$
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
Constant
Linear
RBF
Matern
Kernels
Results
One component at a time
Maruca 2021, Frontiers in A & SS
All components at a time
Qudsi et. al., in prep
Single component input
Vector input
simulation data
simulation data
8 spc
24 spc
8 spc
24 spc
8 spc
16 spc
24 spc
34 spc
24 spc*
22 spc*
Moving Forward
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 ways to compare the reconstructed images for different styles
Thank You!
Magnetore
By Ramiz Qudsi
Magnetore
Discussion of work done towards MagneToRE: the Magnetic Topology Reconstruction Explorer
