Exploring helical dynamos with machine learning

(Click the Binder or Colab links to open the notebooks and work with them in the cloud.)

arxiv.org/abs/1905.08193

Authors: Farrukh Nauman and Joonas Nättilä

Summary: We use regularized linear regression, random forests and Bayesian (Markov Chain Monte Carlo) to select the appropriate model for the turbulent electromotive force that feeds large scale magnetic field growth. We find that regularized linear regression performs the best, and this is due to the low dimensional organized dataset (helically forced turbulence leads to high signal to noise ratio) considered here.

How to get started

1. Download the helically-forced turbulence simulation dataset using the download_data.ipynb notebook.
2. Install external python packages by running pip install -r requirements.txt
3. Explore the data using the provided notebooks!

Content

Currently the analysis consists of:

• temporal and vertical visualizations
  • temporal_profiles.ipynb
  • vertical_profiles.ipynb
• Random forests and LASSO:
  • temporal profile fits
    • Kinematic: rfandlasso_temporal_kinematic.ipynb
    • Close to saturation: rfandlasso_temporal_saturation.ipynb
  • vertical profile fits
    • Linear basis: rfandlasso_vertical_nopoly.ipynb
    • Polynomial basis: rfandlasso_vertical_poly.ipynb
• Bayesian fits (with MCMC) in mcmc.ipynb

Data

Data links are provided here

Simplest way to download files is:

from preprocess import fetch_data
fetch_data() # by default downloads only 4 data files
# Use fetch_data(all=True) to download the entire dataset in the folder alpha2

Some notebooks assume that the data is already downloaded and is in a folder "alpha2/".

If you have trouble running the code, please raise an issue.

Summary of runs reported in the paper

Name	Rm	Rm_t	t_res	v_rms
R5e2	500	1.68	4.97	0.0337
R1e3	1000	4.44	9.94	0.0446
R2e3	2000	10.31	19.88	0.052
R3e3	3000	16.71	30.12	0.055
R4e3	4000	22.64	39.76	0.057
R5e3	5000	28.72	49.70	0.058
R6e3	6000	34.61	59.63	0.058
R7e3	7000	40.41	69.58	0.058
R8e3	8000	46.22	79.52	0.058
R9e3	9000	50.16	89.55	0.056
R1e4*	10000	55.79	99.40	0.056
R15e4*	15000	82.12	149.1	0.055

Data is stored in (compressed) numpy file format. You can load the data using np.load() and see different components with list():

mf15 = np.load('mfields_R15e3.npz')
list(mf15)
# ['tres', Resistive time: 1/(kf^2 * eta) (divide tt by tres to get time array in Resistive times)
  'Rm',   Turbulent magnetic Reynolds number: urms/(kf * eta)
  'uave', RMS velocity: urms
  'kf',   Forcing wavemode
  'tt',   Time array (code units)
  'bxm',  xy-averaged B_x field
  'bym',  xy-averaged B_y field
  'b2tot',xy-averaged B^2 TOTAL field
  'u2tot',xy-averaged U^2 TOTAL field
  'emfx', xy-averaged EMF_x field
  'emfy', xy-averaged EMF_y field
  'jxm',  xy-averaged J_x field
  'jym']  xy-averaged J_y field
  
  z-array can be generated like this:
  z_arr = np.linspace(0,2*np.pi,256)

Each of the fields have a dimension of time x vertical coordinate.

Citing this work

If you find this work useful, please cite this as:

@ARTICLE{2019arXiv190508193N,
       author = {{Nauman}, Farrukh and {N{\"a}ttil{\"a}}, Joonas},
        title = "{Exploring helical dynamos with machine learning}",
      journal = {arXiv e-prints},
     keywords = {Astrophysics - Solar and Stellar Astrophysics, Astrophysics - Astrophysics of Galaxies, Computer Science - Machine Learning},
         year = "2019",
        month = "May",
          eid = {arXiv:1905.08193},
        pages = {arXiv:1905.08193},
archivePrefix = {arXiv},
       eprint = {1905.08193},
 primaryClass = {astro-ph.SR},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190508193N},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}