\n",
+ "This tutorial describes how to use the SMT toolbox with multifidelity data to build a surrogate model \n",
+ "SMT which is a python toolbox for building a surrogate model.
\n",
+ "To use SMT models, please follow this link : https://github.com/SMTorg/SMT/blob/master/README.md. \n",
+ " The doc is available here: http://smt.readthedocs.io/en/latest/\n",
+ "
\n",
+ "\n",
+ "\n",
+ "For the multifidelity extension, a description of the algorithm is available here https://arc.aiaa.org/doi/pdf/10.2514/6.2019-3236"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "slideshow": {
+ "slide_type": "subslide"
+ }
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Requirement already satisfied: smt in d:\\bartoli\\anaconda3\\lib\\site-packages (2.0.1)\n",
+ "Requirement already satisfied: scikit-learn in d:\\bartoli\\anaconda3\\lib\\site-packages (from smt) (1.3.0)\n",
+ "Requirement already satisfied: pyDOE2 in d:\\bartoli\\anaconda3\\lib\\site-packages (from smt) (1.3.0)\n",
+ "Requirement already satisfied: scipy in d:\\bartoli\\anaconda3\\lib\\site-packages (from smt) (1.11.1)\n",
+ "Requirement already satisfied: numpy in d:\\bartoli\\anaconda3\\lib\\site-packages (from pyDOE2->smt) (1.24.3)\n",
+ "Requirement already satisfied: joblib>=1.1.1 in d:\\bartoli\\anaconda3\\lib\\site-packages (from scikit-learn->smt) (1.2.0)\n",
+ "Requirement already satisfied: threadpoolctl>=2.0.0 in d:\\bartoli\\anaconda3\\lib\\site-packages (from scikit-learn->smt) (2.2.0)\n"
+ ]
+ }
+ ],
+ "source": [
+ "!pip install smt"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "\n",
+ "\n",
+ "\n",
+ "# Multi-Fidelity Kriging \n",
+ "\n",
+ "We are interested in learning a high-fidelity function while using low-fidelity information sources to enhance the model, for that we use Le Gratiet recursive formulation of multi-fidelity Kriging.\n",
+ "\n",
+ "
\n",
+ "An important assumption by using this recursive formulation is the nested DOE. \n",
+ "If we have thow fidelity levels (HF and LF)\n",
+ "$$X_{HF} \\subset X_{LF}$$\n",
+ "
\n",
+ "\n",
+ "### Kennedy O'Hagan/Le Gratiet recursive formulation:\n",
+ "To perform Le Gratiet's learning, we first learn the lowest fidelity, then we consecutively learn the relationship between every two consecutive fidelity levels (scaling factor $\\rho_{k-1}$ and discrepancy function $\\delta_k(\\cdot)$).\n",
+ "\n",
+ "$$\\mu_{k} = \\rho_{k-1}\\;\\mu_{k-1} + \\mu_{\\delta_k}\\\\\n",
+ "\\sigma^2_{k} = \\rho_{k-1}^2\\;\\sigma^2_{k-1}+\\sigma^2_{\\delta_k}$$\n",
+ "\n",
+ "![Multi-Fidelity 1-D toy problem](co-krigeage.png)\n",
+ "\n",
+ "This generally results in a better surrogate model compared to training the high-fidelity alone.\n",
+ "\n",
+ "### SMT \n",
+ "SMT is a joint library between NASA, UoM, ONERA and ISAE-SUPAERO. It offers many surrogate modeling tools with a focus on derivatives. Le Gratiet's formulation was implemented as part of SMT.\n",
+ "\n",
+ "After dowmloading and installing SMT library from: https://github.com/SMTorg/smt\n",
+ "\n",
+ "We import the needed packages"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from smt.applications import MFK\n",
+ "import numpy as np\n",
+ "from matplotlib import pyplot as plt\n",
+ "%matplotlib inline"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## 1- Build a multifidelity model using two fidelity levels"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "#defining low and high fidelity functions\n",
+ "def LF_function(x):\n",
+ " return 0.5*((x*6-2)**2)*np.sin((x*6-2)*2)+(x-0.5)*10. - 5\n",
+ "\n",
+ "def HF_function(x):\n",
+ " return ((x*6-2)**2)*np.sin((x*6-2)*2)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, '$y$')"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
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+ "