The documentation can be found here: https://www.egr.msu.edu/coinlab/blankjul/pydacefit/

The purpose of this clone is to have a python version of the popular dacefit toolbox in MATLAB . The toolbox can be found here <https://www.mathworks.com/matlabcentral/fileexchange/38530-surrogate-model-optimization-toolbox>_.

This framework is an exact clone of the original code and the correctness has been checked. Please contact me if you should be scenarios where the values are significantly different ($10^{6}$).

Installation

The test problems are uploaded to the PyPi Repository.

.. code:: bash

pip install pydacefit

Usage

.. code:: python

import numpy as np

from pydacefit.corr import Gaussian, Cubic, Exponential, GeneralizedExponential, Spline, Spherical
from pydacefit.dace import DACE
from pydacefit.regr import ConstantRegression, LinearRegression, QuadraticRegression

import matplotlib.pyplot as plt

# -----------------------------------------------
# Different ways of initialization
# -----------------------------------------------

# kernels and trends are first-class objects -- pass an instance directly.
# regression can be: ConstantRegression(), LinearRegression() or QuadraticRegression()
regression = ConstantRegression()
# regression = LinearRegression()
# regression = QuadraticRegression()


# then define the correlation (all possible correlations are shown below)
# please have a look at the MATLAB document for more details
correlation = Gaussian()
# correlation = Cubic()
# correlation = Exponential()
# correlation = GeneralizedExponential()
# correlation = Spline()
# correlation = Spherical()
# correlation = RationalQuadratic(alpha=0.5)   # alpha is a fixed shape parameter


# This initializes a DACEFIT objective using the provided regression and correlation
# because an initial theta is provided and also thetaL and thetaU the hyper parameter
# optimization is done
dacefit = DACE(regr=regression, corr=correlation,
               theta=1.0, thetaL=0.00001, thetaU=100)

# if no lower and upper bounds are defined, then no hyperparameter optimization is executed
dacefit_no_hyperparameter_optimization = DACE(regr=regression, corr=correlation,
                                              theta=1.0, thetaL=None, thetaU=None)

# to turn on the automatic relevance detection use a vector for theta and define bounds
dacefit_with_ard = DACE(regr=regression, corr=correlation,
                        theta=[1.0, 1.0], thetaL=[0.001, 0.0001], thetaU=[20, 20])


# -----------------------------------------------
# Create some data for the purpose of testing
# -----------------------------------------------

def fun(X):
    return np.sum(np.sin(X * 2 * np.pi), axis=1)


X = np.random.random((20, 1))
F = fun(X)

# -----------------------------------------------
# Fit the model with the data and predict
# -----------------------------------------------

# create the model and fit it
dacefit.fit(X, F)

# predict values for plotting
_X = np.linspace(0, 1, 100)[:, None]
_F = dacefit.predict(_X)

# -----------------------------------------------
# Plot the results
# -----------------------------------------------

plt.scatter(X, F, label="prediction")
plt.plot(_X, _F, label="data")
plt.legend()
plt.show()

print("MSE: ", np.mean(np.abs(fun(_X)[:, None] - _F)))

Contact

Feel free to contact me if you have any question:

| Julian Blank (blankjul [at] egr.msu.edu) | Michigan State University | Computational Optimization and Innovation Laboratory (COIN) | East Lansing, MI 48824, USA