Working example to address the functionality I requested in Issue #213 for the Sobol method

Usage example:

import pandas as pd
from SALib.sample import saltelli
from SALib.analyze import sobol
from SALib.test_functions import Ishigami

X = saltelli.sample(problem, 1000)
Y = Ishigami.evaluate(X)
Si = sobol.analyze(problem, Y, print_to_console=True)

first, (idx, second) = sobol.Si_to_pandas_dict(Si, problem)
first_Si = pd.DataFrame(first, index=problem['names'])
second_Si = pd.DataFrame(second, index=idx)

Hello, Sorry for coming with multiple questions. I am trying to test different methods for sensitivity. I study the sensitivity of max,mean,median and,equilibrium value of the model output. For median value of y2 and some others I got huge positive values and negative values. The values for main effect S1 are reasonable and comparable with sobol and RBD-Fast method. I tested with number of samples 1000,(15000 with resample_number=100,500) and 60000 and no improvement. According to Borgonovo 2007 article delta values should be between 0 and 1. Is there something wrong with my model or implementation of the method? The code

import numpy as np
from numpy import *
from cmath import*
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import scipy as scp
from scipy.integrate import solve_ivp, odeint
import SALib
from SALib.sample import saltelli,morris,latin,ff,finite_diff
from SALib.sample import morris
from SALib.analyze import sobol,dgsm,rbd_fast,delta,ff,dgsm
from SALib.analyze import morris
from SALib.plotting.bar import plot as barplot
from SALib.plotting.morris import *
problem = {
    'num_vars': 11,
    'names': ['$\\beta_{1}$', '$\\beta_{2}$', '$\\epsilon_{1}$','$\\epsilon_{2}$','$g_{12}$','$\gamma_{12}$','$\omega_{11}$','$\omega_{22}$','$x_{0}$','${y_{1}}_{0}$','${y_{2}}_{0}$'],
    'bounds': [[200, 2500000],
               [200, 2500000],
               [0.01, 100],
               [0.01, 100],
               [0.04, 600],
               [0.0002, 20],
               [0.002, 100],
               [0.002, 100],
               [0.0002, 5.71428571],
               [0.01, 2000000],
               [0.01, 2000000]]
}
def dynamical_model_bacteria(t,X,beta1, beta2, epsilon1,epsilon2,g12,gamma12,omega11,omega22):    
    x, y1, y2 = X
    dxdt=x*(1-x-y1-y2)
    dy1dt=y1*(-epsilon1-omega11*y1-g12*y2+beta1*x)
    dy2dt=y2*(-epsilon2+gamma12*y1-omega22*y2+beta2*x)
    return dxdt,dy1dt,dy2dt
def run_model(param_values):
    loop_n = param_values.shape[0]
    x_res = np.empty((loop_n, 4))
    y1_res = np.empty((loop_n, 4))
    y2_res = np.empty((loop_n, 4))
    
    t = [0, 60]
    t_eval_pts = np.linspace(0, 60, 8000)
    for i in range(loop_n):
        beta1, beta2, epsilon1,epsilon2,g12,gamma12,omega11,omega22,x0,y10,y20,*_ = param_values[i]

        X0 = [x0, y10, y20]
        arg_list = (beta1, beta2, epsilon1,epsilon2,g12,gamma12,omega11,omega22)
        sol = solve_ivp(dynamical_model_bacteria, t, X0, args=arg_list, t_eval=t_eval_pts,method='Radau')

        x, y1, y2 = sol.y
        x_res[i, :] = amax(x), mean(x), median(x), x[-1]
        y1_res[i, :] = amax(y1), mean(y1), median(y1), y1[-1]
        y2_res[i, :] = amax(y2), mean(y2), median(y2), y2[-1]
    return x_res, y1_res, y2_res

param_values4 =SALib.sample.latin.sample(problem, 15000)
%%time
xDelta, y1Delta, y2Delta=run_model(param_values4)
%%time
  
DELTA=[i for i in xDelta.T] + [i for i in y1Delta.T] + [i for i in y2Delta.T]
RESULTSDelta=[]
for i, j in zip(DELTA, range(12)):
    Si_Delta= delta.analyze(problem,param_values4, i,num_resamples=500)
    Sidf_Delta= Si_Delta.to_df()
    Sidf_Delta.sort_values(by=['S1'], inplace=True, ascending=False)
    #Renaming the columns names to put them in math notation
    Sidf_DeltaNew=Sidf_Delta.rename(columns={'delta':'$\delta$','delta_conf':'$\delta_{conf}$','S1': '$S_{1}$','S1_conf':'${S_{1}}_{conf}$'})
    RESULTSDelta.append( Sidf_DeltaNew)
    barplot( Sidf_Delta)
    #plt.xlim([-1, 100])
    #plt.ylim([-0.5, 0.7])
    plt.title(TITLE[j] )
    #plt.gcf().set_size_inches(20, 4)

Hi there,

I noted that there are two closed incidents on this topic (#152 and #1510), as well a recent one (#240). But I believe that the issue I'm having is different to those that were reported.

I am using Python 3.6.5 on a windows machine and SALib 1.3.3

I conducted a series of tests using four input parameters to derive a single output. There are four scenarios, so I want to evaluate Delta indices in each scenario for different bootstrap levels by using the following code (note that I consider "resamples" option in Delta index as the number of samples to be taken in bootstrap procedure):

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ problem= { 'num_vars': 5, 'names': ['input_1', 'input_2', 'input_3', 'input_4', 'input_5'], 'bounds': [[min_input_1, max_input_1], [min_input_2, max_input_2], [min_input_3, max_input_3], [min_input_4, max_input_4], [min_input_5, max_input_5]], }

Si= []

filename= 'delta_moment_3d_orig_n_noise_class_' figure_name= 'delta_moment_3d_orig_n_noise_class_'

label= 'Free noise wedge model'

attribute_names= ['input_1', 'input_2', 'input_3', 'input_4', 'input_5']

bootstrap= 0

print("Perform Delta-Moment Independent Test\n")

for count in range(0,len(classification_names)): # Test different scenarios filename= filename + np.str(count + 1) + '.csv' figure_name= figure_name + np.str(count + 1)

output_file= open(path + filename, 'w')

for iters in range(0,4): # Test different bootstrap levels
    bootstrap += 200

    print("using a bootstrap sampling of {} at iteration {} and count {}\n".format(bootstrap, iters, count))

    Si= delta.analyze(problem, attribute_data, classification_data[:,count], num_resamples= bootstrap, print_to_console= True)

    if (bootstrap == 200):
        field_names= []
    
        for key in Si:
            field_names.append(str(key))
        
        output_file.write("%s %s %s %s %s %s %s %s %s %s %s\n" %("attribute name", ',', field_names[0], ',',
                                                                 field_names[1], ',', field_names[2], ',', field_names[3], ',',
                                                                 "bootstrap level"))

    delta_r= Si.get('delta')
    delta_conf_r= Si.get('delta_conf')
    sobol_r= Si.get('S1')
    sobol_conf_r= Si.get('S1_conf')

    for i in range(0, len(delta_r)):
        output_file.write("%s %s %2.5f %s %2.5f %s %2.5f %s %2.5f %s %s\n" %(attribute_names[i], ',', delta_r[i], 
                                                                         ',', delta_conf_r[i], ',', sobol_r[i], ',',
                                                                         sobol_conf_r[i], ',', str(bootstrap)))
    
    print("\n")

output_file.close()

SA= pd.read_csv(path + filename, delimiter= ',')
plot_histograms(SA, label, figure_name)

filename= 'delta_moment_3d_orig_n_noise_class_'
figure_name= 'delta_moment_3d_orig_n_noise_class_'

Si= []

bootstrap= 0

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

So, I checked for bootstrap levels at 200, 400, 600, and 800. All input data are 1D arrays of length 20099 samples. When the script reaches the second scenario for a bootstrap of 600, the following error message occurs:

using a bootstrap sampling of 600 at iteration 2 and count 2

Parameter delta delta_conf S1 S1_conf Input_1 0.313084 0.004628 0.081716 0.010388 Input_2 0.436194 0.008330 0.371258 0.012746

Traceback (most recent call last): File "C:\Temp\Python\Python36\lib\site-packages\SALib\analyze\delta.py", line 75, in analyze Y, Ygrid, X[:, i], m, num_resamples, conf_level) File "C:\Temp\Python\Python36\lib\site-packages\SALib\analyze\delta.py", line 115, in bias_reduced_delta d[i] = calc_delta(Y[r], Ygrid, X[r], m) File "C:\Temp\Python\Python36\lib\site-packages\SALib\analyze\delta.py", line 101, in calc_delta fyc = gaussian_kde(Y[ix], bw_method='silverman')(Ygrid) File "C:\Temp\Python\Python36\lib\site-packages\scipy\stats\kde.py", line 172, in init self.set_bandwidth(bw_method=bw_method) File "C:\Temp\Python\Python36\lib\site-packages\scipy\stats\kde.py", line 499, in set_bandwidth self._compute_covariance() File "C:\Temp\Python\Python36\lib\site-packages\scipy\stats\kde.py", line 510, in _compute_covariance self._data_inv_cov = linalg.inv(self._data_covariance) File "C:\Temp\Python\Python36\lib\site-packages\scipy\linalg\basic.py", line 975, in inv raise LinAlgError("singular matrix") numpy.linalg.linalg.LinAlgError: singular matrix

During handling of the above exception, another exception occurred:

Traceback (most recent call last): File "Run_sa_3d_results.py", line 202, in Si= delta.analyze(problem, attribute_data, classification_data[:,count], num_resamples= bootstrap, print_to_console= True) File "C:\Temp\Python\Python36\lib\site-packages\SALib\analyze\delta.py", line 85, in analyze raise np.linalg.LinAlgError(msg) numpy.linalg.linalg.LinAlgError: Singular matrix detected Sample size of 20099 may be too small

For some reason, Delta function considers that there not enough samples. However, the script was able to perform 10 computations.

In the attached file, you will find the input data: A) Model input: input_1, input_2, input_3, input_4, input_5 B) Model output: output_1, output_2, output_3, output_4 C) Python script

Many thanks for your help!

Ivan

Delta_indices.zip

Hello, I compare some tools and methods to calculate Sobol indices and I got some strange values for first order indices with SALib.

With Polynomial Chaos (openturns) and EASI algorithm, I have the following results for S1's:

    Polynomial Chaos    EASI
x1  0.48                0.48
x2  0.25                0.25
x3  0.10                0.11
x4  0.04                0.05
x5  0.04                0.04
x6  0.03                0.03
x7  0.02                0.02
x8  0.02                0.02
x9  0.02                0.02
x10 0.01                0.01

As you can see, they converge to the same values. And 500 simulations with a Quasi Monte-Carlo sample is enough to reach these values (I tried up to 2000 simulations and they remain the same). Also, the ST's I got with Polynomial Chaos are similar to the S1's (EASI doesn't include this calculation).

With Salib I use saltelli.sample to generate 5000 samples and I have the following results:

    S1      S1_conf  ST  ST_conf
x1  0.92    4.99    0.53    0.06
x2  0.29    2.37    0.16    0.02
x3  0.22    1.70    0.11    0.01
x4  0.25    1.24    0.05    0.01
x5  0.04    1.14    0.04    0.01
x6  0.03    0.98    0.03    0.00
x7  -0.09   1.01    0.02    0.00
x8  0.05    0.98    0.02    0.00
x9  0.06    0.83    0.02    0.00
x10 0.02    0.82    0.01    0.00

Except for the second parameter, the ST's are really close to what I got with other methods. However, the S1's don't look good and the confidence intervals are terrible. I don't understand why SALib is able to calculate ST's but not S1's in my case, specially if they have similar values. I could increase the sample size but 5000 took 80 hours... Any thoughts on this issue ?

Hello everyone,

I have used this package with great pleasure so far. In my internship I am going to implement the Morris method on a complex model, but while reading the scientific literature I found some methods that, in my opinion, would make a nice addition to this package. I am not sure if this is the right place to post this; so if I am doing this incorrectly, sorry in advance. I am not a very skilled coder, therefore I mention these methods here. I hope my lazy attitude does not bother you! ;-)

--Radial Sampling-- This is nothing else than an iterated One Factor At A Time approach. Starting from a random point in the hyperspace, one step in turn is taken for each factor. This procedure is iterated. So: instead of using trajectories like Morris' method, "stars" are created in the input hyperspace. Campolongo et al. (2011) used this method with greater success than Morris' method and the same amount of runs. http://www.sciencedirect.com/science/article/pii/S0010465510005321

--Morris method with sampling strategy of Ruano et al. (2012)-- As the "Brute Force Approach" of Campolongo et al. (2007) introduces an combinatorial optimization problem, a sampling strategy which looks at combinations locally instead of globally might be a nice addition to the Morris function in this package. This makes it doable to create more optimized trajectories in exchange for a better coverage of the input space. Still, this is better than purely random sampling. Ruano et al. (2012) present such an approach. I myself find it hard to understand the thoughts behind each step in their algorithm, but it is presented in such a way that it could be implemented in code. http://www.sciencedirect.com/science/article/pii/S1364815212000904 UPDATE: I have made an implementation of this method for SALib and pulled it as a request (or whatever the correct grammar for a "pull request" is)

--Latin Hypercube Sampling (LHS) of starting points in Morris method-- Using LHS for the starting points was originally proposed by Morris to enhance the spread in the output space. This is also an alternative to the "brute force approach".

I hope these methods could be added to the "Methods to consider adding" list! If you cannot access the papers, send me a message.

• Added groups functionality to Morris (#24) - 06ed41a
• Wrapped all the different Morris sampling methods in a class called Morris. - cb12326
• Added a template class called Sample from which all sampling methods can inherit shared methods (such as reading a parameter file, saving the sample to disk)
• Added some more tests (for test_functions) - f8c1727
• Added read_group_file to utils. At present, you need to pass a k-by-g matrix, where each row denotes membership of group in column g. - 5cbd77f

Use

Generating a sample is still easy from within python:

sample = Morris(paramfile, samples, levels, grid_jump, group, k_optimal)
# Save the data to disk
sample.save_data(output_filename, delimiter, precision)
# Or get the sample as a numpy array
sample.get_input_sample_scaled()
# Or
sample.get_input_sample_unscaled()

And just as easy on the command line (and unchanged from previous versions):

python -m SALib.sample.morris -n=100 -p=SALib/tests/test_params.txt --output=foo.txt -s=123 -k=1 --group=groups.txt

Note the arguments -k and --group are optional. Including them activates the respective method of sampling.

A group file can be csv, tab-delimted or whitespace delimited and should be of the format"

Factor1 1 0
Factor2 0 1
Factor3 0 1

to create two groups, of which Factor1 is a member of group 1 (column 1), and Factors 2 and 3 are members of group 2 (column 2).

Utils

• Added tests for read file
• Added test and new procedure to read in group files
• Amended the read file procedure so that it sniffs for the type of csv file (python standard library) (#21).

Admin

• Excluded the tests folder from coverage
• Added other exclusions of irrelevant code to .coveragc config file

Remaining work

• The code for the methods of the different Morris sampling methods still resides in each of the original python files. These could be brought into the Morris class.
• There are opportunities for sharing more code between Morris groups and Morris. I have used numpy matrix calculations for computing Morris groups (which uses an only slightly different method to straight-up Morris), and no loops. I've also chunked the code a fair bit to assist with testing.
• Could add checks to ensure that the group file and parameter file factor names match, as well as sense checking for numbers of groups versus number of parameters.

Closes #524 and closes #355

This does 2 things:

• Use Hatchling and doing so removes all extra files which are not needed anymore.
• Migrate from Travis to GitHub Actions: 3 actions are used for linting, testing and deploying.

#519 and #522 would need to be slightly adapted depending on which PR gets in first.

Also, PyPi secrets would need to be added to the repo for deploying.

I simplified the version handling as well. I don't think there is a need to complicate this more. Also note that this is more or less for legacy use as the new way to check that is to rely on package's metadata.

1. Write down list of steps to take when preparing for a new release
2. Create an Issue Template which can be used to keep track of these steps for each release (e.g. a new issue using the template is opened when preparing a release, and closed upon release).

I added a way to find the local maximum distance after Ruano et al. 2012, as alternative to the brute force approach of Campolongo et al. It speeds up the process for especially more trajectories, which can be read in their paper:

"An improved sampling strategy based on trajectory design for application of the Morris method to systems with many input factors". (2012) Environmental Modelling & Software 37

It is now possible to optimize for more than 8 trajectories, without the use of commercial software (Gurobi). The method does not necessarily always find the largest global distance between trajectories, but it still does a good job and is preferable over not doing any optimization.

I am looking forward to your feedback on my coding.

I recently upgrade to SAlib 1.4.0.2 and witnessed a behaviour that looks incorrect to me. When using saltelli.sample, most of the returned samples are identical, which would mean that the model is evaluated several times with the exact same input variables. Is this really how it should be?

Code from the SAlib example:

from SALib.sample import saltelli
from SALib.analyze import sobol

problem = {
    'num_vars': 3,
    'names': ['x1', 'x2', 'x3'],
    'bounds': [[-3.14159265359, 3.14159265359],
               [-3.14159265359, 3.14159265359],
               [-3.14159265359, 3.14159265359]]
}

x = saltelli.sample(problem, 2)

Output:

x = array([[-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [-3.14159265, -3.14159265, -3.14159265],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ]])

Hello !

I have implemented the RBD-FAST algorithm following the SALib contributor guide. I have updated analyzer, examples, docs, examples and tests. The CLI is working. We use the LHS sampler, already implemented in SALib.

I also fixed a little mistake on the latin sampler CLI : the args were parsed before the nsampler arg addition.

I only did the programming work here : many thanks to J. Goffart and M. Rabouille for the matlab implementation and S. Juricic for a first python implementation.

Nicolas Cellier

Documentation with regard to usage and interpretation of Sobol' analysis should be expanded.

See issue raised in #549 as an example of what users may face.

Although this is a general issue across the SALib package, lets start with Sobol'.

I've also posted a more general version of this question on Cross Validated (stats.stackoverflow), here Is it possible in SALib to scale the outputs (mu, mu_star, sigma) of SALib.analyze.morris, so that the sensitivity of different quantities of interest can be compared? I couldn't find anything about this in the docs, is there a way to achieve this?

Okay, I reinstalled my conda environment, built the docs locally and had a brief scan through. The new theme looks great, and nice that we're joining the look-and-feel of the pydata stack.

conda env create -f environment.yml
conda activate salib
cd docs
make html
open _build/html/index.html

Sphinx itself spits out a lot of warnings and a few errors which we should slowly look into:

Running Sphinx v5.1.1
Creating file docs/api/SALib.rst.
Creating file docs/api/SALib.analyze.rst.
Creating file docs/api/SALib.plotting.rst.
Creating file docs/api/SALib.sample.rst.
Creating file docs/api/SALib.sample.morris.rst.
Creating file docs/api/SALib.scripts.rst.
Creating file docs/api/SALib.test_functions.rst.
Creating file docs/api/SALib.util.rst.
Creating file docs/api/modules.rst.
loading pickled environment... failed
failed: No module named 'myst_parser.main'
loading intersphinx inventory from https://www.sphinx-doc.org/en/master/objects.inv...
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[autosummary] generating autosummary for: advanced.rst, api.rst, api/SALib.analyze.rst, api/SALib.plotting.rst, api/SALib.rst, api/SALib.sample.morris.rst, api/SALib.sample.rst, api/SALib.scripts.rst, api/SALib.test_functions.rst, api/SALib.util.rst, api/modules.rst, authors.rst, basics.rst, changelog.md, citations.rst, getting-started.rst, index.rst, license.rst
myst v0.18.0: MdParserConfig(commonmark_only=False, gfm_only=False, enable_extensions=[], disable_syntax=[], all_links_external=False, url_schemes=('http', 'https', 'mailto', 'ftp'), ref_domains=None, highlight_code_blocks=True, number_code_blocks=[], title_to_header=False, heading_anchors=None, heading_slug_func=None, footnote_transition=True, words_per_minute=200, sub_delimiters=('{', '}'), linkify_fuzzy_links=True, dmath_allow_labels=True, dmath_allow_space=True, dmath_allow_digits=True, dmath_double_inline=False, update_mathjax=True, mathjax_classes='tex2jax_process|mathjax_process|math|output_area')
building [mo]: targets for 0 po files that are out of date
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reading sources... [100%] license                                                                             
docs/advanced.rst:43: ERROR: Unexpected indentation.
docs/../src/SALib/analyze/fast.py:docstring of SALib.analyze.fast.analyze:27: WARNING: Duplicate explicit target name: "1".
docs/../src/SALib/analyze/fast.py:docstring of SALib.analyze.fast.analyze:33: WARNING: Duplicate explicit target name: "2".
docs/../src/SALib/sample/latin.py:docstring of SALib.sample.latin.sample:16: WARNING: Duplicate explicit target name: "1".
docs/../src/SALib/sample/latin.py:docstring of SALib.sample.latin.sample:22: WARNING: Duplicate explicit target name: "2".
docs/../src/SALib/analyze/rbd_fast.py:docstring of SALib.analyze.rbd_fast.analyze:29: WARNING: Duplicate explicit target name: "1".
docs/../src/SALib/analyze/rbd_fast.py:docstring of SALib.analyze.rbd_fast.analyze:34: WARNING: Duplicate explicit target name: "2".
docs/../src/SALib/analyze/rbd_fast.py:docstring of SALib.analyze.rbd_fast.analyze:38: WARNING: Duplicate explicit target name: "3".
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:71: WARNING: Duplicate explicit target name: "1".
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:76: WARNING: Duplicate explicit target name: "2".
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:78: ERROR: Unexpected indentation.
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:79: WARNING: Block quote ends without a blank line; unexpected unindent.
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:82: WARNING: Duplicate explicit target name: "3".
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:84: ERROR: Unexpected indentation.
docs/../src/SALib/sample/morris/morris.py:docstring of SALib.sample.morris.morris.sample:86: WARNING: Block quote ends without a blank line; unexpected unindent.
docs/../src/SALib/analyze/morris.py:docstring of SALib.analyze.morris.analyze:60: WARNING: Duplicate explicit target name: "1".
docs/../src/SALib/analyze/morris.py:docstring of SALib.analyze.morris.analyze:63: WARNING: Definition list ends without a blank line; unexpected unindent.
docs/../src/SALib/analyze/morris.py:docstring of SALib.analyze.morris.analyze:66: WARNING: Duplicate explicit target name: "2".
docs/../src/SALib/analyze/morris.py:docstring of SALib.analyze.morris.analyze:69: WARNING: Definition list ends without a blank line; unexpected unindent.
docs/../src/SALib/sample/saltelli.py:docstring of SALib.sample.saltelli.sample:49: WARNING: Duplicate explicit target name: "1".
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build succeeded, 102 warnings.

The HTML pages are in _build/html.

Originally posted by @willu47 in https://github.com/SALib/SALib/issues/523#issuecomment-1240532941

Hi,

I was wondering how do you guys think of having a logo for SALib project. It might be good to put it on the readthedocs page. I found Adobe's online platform that allows you to make logo for free. Here is the link to that page: https://www.adobe.com/express/create/logo

I created one logo on this website. What do you guys think? Do you have any input on the design? I thought having a pie chart on the logo would be nice because of apportioning model outputs to the its inputs. I am leaving two samples here.