Tuning Parameters with NOMAD

In this example in order to test the ability of NOMAD to predict the unknowns variables of the beam model (Detector dead time, Source activity, Reactor attenuation coefficient ) from noisy data, we have generated an artificial set of experimental counts which are exposed to the noise. To generate this data set we have applied noise on particle positions with a normal distribution (mu = 0, sigma = 2 mm), then we have calculated the counts on the new set of particle positions. Using the real particle positions with noisy counts provides us the opportunity of testing NOMAD on noisy experimental data set.

Parameter file

In the subsection “rpt parameters”, we define a set of real positions (theoretical values of inside the reactor. Common parameters for the RPT simulation are described in the RPT parameters subsection in the RPT Parameters documentation.

Note : verbosity MUST be quiet since NOMAD get the cost function value in terminal for its MADS algorithm.

# --------------------------------------------------
# RPT Monte Carlo technique
#---------------------------------------------------
subsection rpt parameters
    set particle positions file          = real_positions.particle
    set verbosity                        = quiet
    set export counts                    = true
    set counts file                      = run.csv
    set monte carlo iteration            = 10000
    set random number seed               = 0
    set reactor radius       		 = 0.1
    set peak-to-total ratio  		 = 0.4
    set sampling time        		 = 1
    set gamma-rays emitted        	 = 2
    set attenuation coefficient detector = 21.477
    set dead time       		 = 1e-5
    set activity  			 = 2e6
    set attenuation coefficient reactor  = 10
end

In the subsection “parameter tuning”, we enable parameters tuning, specify a type of cost function and define a set of artificial counts to compare with calculated counts. Parameters used of the tuning of the model parameters are described in the RPT Parameters documentation.

# --------------------------------------------------
# Initial value of parameters for tuning
#---------------------------------------------------
subsection parameter tuning
	set tuning                           = true
	set cost function type               = larachi
	set experimental data file           = noisy_counts.experimental
end

In the subsection “detector parameters”, we specify the file that contains the position of the detector face center and the position of a point inside the detector on its axis. In this example, the detector face center position is [0.2,0,0.075] and [0.2381,0,0.075] is another point on the detector’s axis. The detector parameters are described in the RPT Parameters documentation.

#---------------------------------------------------
# Detector parameters
#---------------------------------------------------
    set detector positions file          = positions.detector
    set radius       			 = 0.0381 
    set length                           = 0.0762
end

READ ME file

To use NOMAD with the rpt_3d application you need to :

• Modify the paths in script "rpt_nomad_lethe.py"
• Modify the initial guess of parameters and number of black box evaluations for NOMAD in "param_nomad.txt"
• Run NOMAD with its parameter file with => /path/to/NOMAD/ param_nomad.txt

How it works :

• NOMAD will execute the Python script which in provided by the "param_nomad.txt" file.
• The Python script "rpt_nomad_lethe.py" proceeds the values of parameters to tune gave by NOMAD, modifies the parameter file for Lethe and runs the rpt_3d application.
• rpt_3d of Lethe executes the Monte Carlo ray model and calculates a cost function which is got by NOMAD
• NOMAD executes its MADS algorithm and generates new set of parameters until a criteria

Note : Two files are not used in the example execution but are still provided in the current directory. "noisy_positions.particle" keeps track of the positions used to generate noisy_counts.experimental and "real_counts.experimental" are results of artificial data with no noise with 10 000 000 MC iterations.

Results

The best feasible solution reported by NOMAD gives the following values for each unknown.

# --------------------------------------------------
# Best feasible solution
#---------------------------------------------------
	Detector dead time                   = 1.064e-5
	Source activity                      = 2.03125e6
	Reactor attenuation coefficient      = 10.1539

The real values to generate the artificial data set as mentioned in parameter file section are:

# --------------------------------------------------
# Real values for generating data set
#---------------------------------------------------
	Detector dead time                   = 1e-5
	Source activity                      = 2e6
	Reactor attenuation coefficient      = 10