Gaussian Process Regression for Magnetic Field Reconstruction

Ramiz A. Qudsi

Dept. of Phys. and Astronomy, University of Delaware,  DE, USA  

ahmadr@udel.edu

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, 10]~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

Spacecraft

https://slides.com/qudsi/simpex

Gaussian Process Regression Interpolation

Original Data

CK+RBF

RBF

16 Spacecrafts

Hub

Spacecrafts

Hub

Spacecrafts

\rm{Spacecraft}
22\,d_{\rm i}
22\,d_{\rm i}
22\,d_{\rm i}
22\,d_{\rm i}
\rm(a)
\rm(b)

Original Data

RBF (16 spc)

RBF (25 spc)

Simulation

16 spc, RBF

25 spc, RBF

Simulation

RBF (3D)

Original

ck_RQ

ck_Matern

RBF

Original

ck_RQ

ck_Matern

RBF

Original

ck_RQ

ck_Matern

RBF

Original

ck_RQ

ck_Matern

RBF

8 spc

16 spc

24,34 spc

Error Analysis

(kind of)

Distribution of x-component of field

4 spc

8 spc

16 spc

32 spc

24 spc

Distribution of y-component of field

4 spc

8 spc

16 spc

32 spc

24 spc

Distribution of z-component of field

4 spc

8 spc

16 spc

32 spc

24 spc

Distribution of magnitude of field

4 spc

8 spc

16 spc

32 spc

24 spc

Distribution of divergence of field

4 spc

8 spc

16 spc

32 spc

24 spc

Distribution of error in x-component of B

Distribution of error in y-component of B

Distribution of error in z-component of B

Distribution of error in B

Gaussian Processes: Notes