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Workflow to solve v_inner boundary

The source code for this workflow can be found at: https://github.com/tardis-sn/tardis/blob/master/tardis/workflows/v_inner_solver.py.

This workflow demonstrates how to use the TARDIS modules to perform targeted tasks. This workflow is built on top of the SimpleTARDISWorkflow to solve the v_inner boundary, in addition to the remaining radiative properties.

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from astropy import units as u

from tardis.workflows.v_inner_solver import InnerVelocitySolverWorkflow
from tardis.io.configuration.config_reader import Configuration

/home/runner/work/tardis/tardis/tardis/__init__.py:17: UserWarning: Astropy is already imported externally. Astropy should be imported after TARDIS.
  warnings.warn(

config = Configuration.from_yaml('../tardis_example.yml')

This code modifies the TARDIS example configuration to include convergence information for the inner boundary velocity solver.

config.montecarlo.convergence_strategy['v_inner_boundary'] = {
    'damping_constant' : 0.5,
    'threshold' : 0.01,
    'type' : 'damped',
    'store_iteration_properties' : True
    }

config.montecarlo.convergence_strategy.stop_if_converged = True
config.model.structure.velocity.start = 5000 * u.km/u.s # Decrease start velocity from 11000 km/s in example file, to search over a wider range
config.model.structure.velocity.num = 50 # Increase number of shells from 20 in example file, to provide more granularity

workflow = InnerVelocitySolverWorkflow(
    config, tau=2.0/3,
    mean_optical_depth="rosseland"
)

workflow.run()

Shell No.	t_rad	next_t_rad	w	next_w
0	1.44e+04 K	1.59e+04 K	0.0531	0.485
5	1.44e+04 K	1.66e+04 K	0.0407	0.214
10	1.43e+04 K	1.68e+04 K	0.0323	0.125
15	1.42e+04 K	1.63e+04 K	0.0262	0.0917
20	1.42e+04 K	1.57e+04 K	0.0217	0.0755
25	1.41e+04 K	1.5e+04 K	0.0183	0.0669

Shell No.	t_rad	next_t_rad	w	next_w
0	1.59e+04 K	1.24e+04 K	0.485	0.461
5	1.66e+04 K	1.38e+04 K	0.214	0.16
10	1.68e+04 K	1.39e+04 K	0.125	0.0937
15	1.63e+04 K	1.38e+04 K	0.0917	0.0666
20	1.57e+04 K	1.34e+04 K	0.0755	0.0551
25	1.5e+04 K	1.28e+04 K	0.0669	0.0492

Shell No.	t_rad	next_t_rad	w	next_w
0	1.24e+04 K	1.14e+04 K	0.461	0.512
5	1.38e+04 K	1.25e+04 K	0.16	0.199
10	1.39e+04 K	1.28e+04 K	0.0937	0.111
15	1.38e+04 K	1.27e+04 K	0.0666	0.0776
20	1.34e+04 K	1.23e+04 K	0.0551	0.0632
25	1.28e+04 K	1.19e+04 K	0.0492	0.0561

Shell No.	t_rad	next_t_rad	w	next_w
0	1.14e+04 K	1.12e+04 K	0.512	0.508
5	1.25e+04 K	1.18e+04 K	0.199	0.226
10	1.28e+04 K	1.2e+04 K	0.111	0.135
15	1.27e+04 K	1.21e+04 K	0.0776	0.0899
20	1.23e+04 K	1.18e+04 K	0.0632	0.0736
25	1.19e+04 K	1.14e+04 K	0.0561	0.0651

Shell No.	t_rad	next_t_rad	w	next_w
0	1.12e+04 K	1.09e+04 K	0.508	0.532
5	1.18e+04 K	1.14e+04 K	0.226	0.235
10	1.2e+04 K	1.15e+04 K	0.135	0.145
15	1.21e+04 K	1.14e+04 K	0.0899	0.106
20	1.18e+04 K	1.12e+04 K	0.0736	0.0848
25	1.14e+04 K	1.08e+04 K	0.0651	0.0749

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.09e+04 K	0.532	0.509
5	1.14e+04 K	1.12e+04 K	0.235	0.241
10	1.15e+04 K	1.12e+04 K	0.145	0.153
15	1.14e+04 K	1.1e+04 K	0.106	0.114
20	1.12e+04 K	1.08e+04 K	0.0848	0.0915
25	1.08e+04 K	1.05e+04 K	0.0749	0.0792

Shell No.	t_rad	next_t_rad	w	next_w
0	1.45e+04 K	1.08e+04 K	0.0563	0.561
5	1.13e+04 K	1.13e+04 K	0.263	0.25
10	1.12e+04 K	1.13e+04 K	0.162	0.155
15	1.11e+04 K	1.11e+04 K	0.12	0.115
20	1.09e+04 K	1.08e+04 K	0.0945	0.0928
25	1.06e+04 K	1.06e+04 K	0.081	0.0796
30	1.02e+04 K	1.03e+04 K	0.0744	0.0702

Shell No.	t_rad	next_t_rad	w	next_w
0	1.08e+04 K	1.09e+04 K	0.561	0.578
5	1.13e+04 K	1.14e+04 K	0.25	0.253
10	1.13e+04 K	1.14e+04 K	0.155	0.156
15	1.11e+04 K	1.12e+04 K	0.115	0.115
20	1.08e+04 K	1.09e+04 K	0.0928	0.0957
25	1.06e+04 K	1.07e+04 K	0.0796	0.08
30	1.03e+04 K	1.04e+04 K	0.0702	0.0716

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.1e+04 K	0.578	0.57
5	1.14e+04 K	1.13e+04 K	0.253	0.255
10	1.14e+04 K	1.14e+04 K	0.156	0.157
15	1.12e+04 K	1.12e+04 K	0.115	0.116
20	1.09e+04 K	1.09e+04 K	0.0957	0.0938
25	1.07e+04 K	1.07e+04 K	0.08	0.0802
30	1.04e+04 K	1.03e+04 K	0.0716	0.0718

Shell No.	t_rad	next_t_rad	w	next_w
0	1.1e+04 K	1.09e+04 K	0.57	0.565
5	1.13e+04 K	1.14e+04 K	0.255	0.25
10	1.14e+04 K	1.14e+04 K	0.157	0.158
15	1.12e+04 K	1.11e+04 K	0.116	0.119
20	1.09e+04 K	1.1e+04 K	0.0938	0.0935
25	1.07e+04 K	1.06e+04 K	0.0802	0.081
30	1.03e+04 K	1.03e+04 K	0.0718	0.0731

Plot the spectrum

spectrum = workflow.spectrum_solver.spectrum_real_packets
spectrum_virtual = workflow.spectrum_solver.spectrum_virtual_packets
# spectrum_integrated = workflow.spectrum_solver.spectrum_integrated

%matplotlib inline
plt.figure(figsize=(10, 6.5))

spectrum.plot(label="Normal packets")
spectrum_virtual.plot(label="Virtual packets")
# spectrum_integrated.plot(label='Formal integral')

plt.xlim(500, 9000)
plt.title("TARDIS example model spectrum")
plt.xlabel(r"Wavelength [$\AA$]")
plt.ylabel(r"Luminosity density [erg/s/$\AA$]")
plt.legend()
plt.show()

Plot the convergence process

%matplotlib inline

# extract plasma states
t_rad = workflow.iterations_t_rad
t_inner = workflow.iterations_t_inner
w = workflow.iterations_w
taus = workflow.iterations_mean_optical_depth
v_inner = workflow.iterations_v_inner_boundary

# remove all nans, or rows where all values are nan
t_rad = t_rad[~np.all(np.isnan(t_rad), axis=1)]
t_inner = t_inner[~np.isnan(t_inner)]
w = w[~np.all(np.isnan(w), axis=1)]
taus = taus[~np.all(np.isnan(taus), axis=1)]
v_inner = v_inner[~np.isnan(v_inner)]

# initialize figure
fig,axes =  plt.subplots(2,2,figsize=(12,8))
plt.subplots_adjust(wspace=0.4,hspace=0.3)

# get the raw velocity grid
vel = workflow.simulation_state.geometry.v_inner

# pick a colormap for the iterations
cmap = plt.get_cmap('plasma',taus.shape[0])

# plot v inner change
v_inner_plot = axes[0,0]
v_inner_plot.plot(v_inner,marker="o",color="b")
v_inner_plot.set_xlabel("Iterations", fontsize=14)
v_inner_plot.set_ylabel("v_inner (cm/s)", fontsize=14)
v_inner_plot.grid(alpha=0.3)
v_inner_plot.tick_params(axis='y', colors='blue')
v_inner_plot.yaxis.label.set_color('blue')

# plot t inner change in same subplot
t_inner_plot = axes[0][0].twinx()
t_inner_plot.plot(t_inner,marker="s",color="r")
t_inner_plot.set_ylabel("t_inner (K)", fontsize=14)
t_inner_plot.tick_params(axis='y', colors='red')
t_inner_plot.yaxis.label.set_color('red')

# plot the tau change
tau_plot = axes[0][1]
for i, tau in enumerate(taus):
    tau_plot.plot(vel[-len(tau):], tau, color=cmap(i/taus.shape[0]),label=f"itr {i+1}",alpha=0.7)
tau_plot.scatter(workflow.simulation_state.v_inner_boundary.value, np.log(2.0 / 3.0), color="k",marker="o")
tau_plot.axhline(np.log(2.0 / 3.0), color='black', linestyle='--')
tau_plot.axvline(workflow.simulation_state.v_inner_boundary.value, color='k', linestyle='--')
tau_plot.set_xlabel("Velocity (cm/s)", fontsize=14)
tau_plot.set_ylabel("log(tau)", fontsize=14)
tau_plot.grid(alpha=0.3)
tau_plot.set_title("1 Loop of all together - without resetting plasma", fontsize=14)

# plot t radiative change
t_rad_plot = axes[1][0]
for i in range(len(taus)):
    t_rad_plot.plot(vel[-len(t_rad[i]):], t_rad[i],color=cmap(i/taus.shape[0]),label=f"itr {i+1}",alpha=0.7)
t_rad_plot.set_xlabel("Velocity (cm/s)", fontsize=14)
t_rad_plot.set_ylabel("t_rad", fontsize=14)
t_rad_plot.grid(alpha=0.3)

# plot dilution factor change
w_plot = axes[1][1]
for i in range(len(taus)):
    w_plot.plot(vel[-len(w[i]):], w[i],color=cmap(i/taus.shape[0]),label=f"itr {i+1}",alpha=0.7)
w_plot.set_xlabel("Velocity (cm/s)", fontsize=14)
w_plot.set_ylabel("dilution_factor", fontsize=14)
w_plot.grid(alpha=0.3)

# add colorbar for iteration number
norm = mpl.colors.Normalize(vmin=1, vmax=len(taus))
sm = mpl.cm.ScalarMappable(cmap=cmap, norm=norm)
cbar = fig.colorbar(sm, ax=axes, orientation='vertical', fraction=0.025, pad=0.02)
cbar.set_label('Iteration Number', fontsize=12)