tutorials/tutorial-2.ipynb

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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#EZyRB-Tutorial-2\" data-toc-modified-id=\"EZyRB-Tutorial-2-1\">EZyRB Tutorial 2</a></span><ul class=\"toc-item\"><li><span><a href=\"#Test-several-frameworks-at-once\" data-toc-modified-id=\"Test-several-frameworks-at-once-1.1\">Test several frameworks at once</a></span><ul class=\"toc-item\"><li><span><a href=\"#Initial-setting\" data-toc-modified-id=\"Initial-setting-1.1.1\">Initial setting</a></span></li><li><span><a href=\"#Comparison-between-different-methods\" data-toc-modified-id=\"Comparison-between-different-methods-1.1.2\">Comparison between different methods</a></span></li></ul></li></ul></li></ul></div>"
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    "# EZyRB Tutorial 2\n",
    "## Test several frameworks at once\n",
    "\n",
    "In this tutorial, we will explain step by step how to use the **EZyRB** library to test different techniques for building the reduced order model. We will compare different methods of dimensionality reduction, interpolation and accuracy assessment.\n",
    "\n",
    "We consider here a computational fluid dynamics problem described by the (incompressible) Navier Stokes equations.\n",
    "We will be using the **Navier Stokes Dataset** that contains the output data from a full order flow simulation and can be found on **GitHub** under [Smithers library](https://github.com/mathLab/Smithers).\n",
    "**Smithers** is developed by **SISSA mathlab** and it contains some useful datasets and a multi-purpose toolbox that inherits functionality from other packages to make the process of dealing with these datasets much easier with more compact coding.\n",
    "\n",
    "The package can be installed using `python -m pip install smithers -U`, but for a detailed description about installation and usage we refer to original [Github page](https://github.com/mathLab/Smithers/blob/master/README.md).\n",
    "\n",
    "First of all, we just import the package and instantiate the dataset object."
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2b772df3",
   "metadata": {},
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   "source": [
    "from smithers.dataset import NavierStokesDataset\n",
    "data = NavierStokesDataset()"
   ]
  },
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   "id": "26eba516",
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   "source": [
    "The `NavierStokesDataset()` class contains the attribute:\n",
    "- `snapshots`: the matrices of snapshots stored by row (one matrix for any output field)\n",
    "- `params`: the matrix of corresponding parameters\n",
    "- `pts_coordinates`: the coordinates of all nodes of the discretize space\n",
    "- `faces`: the actual topology of the discretize space\n",
    "- `triang`: the triangulation, useful especially for rendering purposes.\n",
    "\n",
    "In the details, `data.snapshots` is a dictionary with the following output of interest:\n",
    "- **vx:** velocity in the X-direction. \n",
    "- **vy:** velocity in the Y-direction. \n",
    "- **mag(v):** velocity magnitude.\n",
    "- **p:** pressure value.\n",
    "\n",
    "In total, the dataset contains 500 parametric configurations in a space of 1639 degrees of freedom. In this case, we have just one parameter, which is the velocity (along $x$) we impose at the inlet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b8d8c9b8",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of vx      snapshots matrix: (500, 1639)\n",
      "Shape of vy      snapshots matrix: (500, 1639)\n",
      "Shape of p       snapshots matrix: (500, 1639)\n",
      "Shape of mag(v)  snapshots matrix: (500, 1639)\n",
      "Shape of parameters matrix: (500, 1)\n"
     ]
    }
   ],
   "source": [
    "for name in ['vx', 'vy', 'p', 'mag(v)']:\n",
    "    print('Shape of {:7s} snapshots matrix: {}'.format(name, data.snapshots[name].shape))\n",
    "    \n",
    "print('Shape of parameters matrix: {}'.format(data.params.shape))\n"
   ]
  },
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   "source": [
    "### Initial setting\n",
    "\n",
    "First of all, we import the required packages.\n",
    "\n",
    "From `EZyRB` we need:\n",
    "1. The `ROM` class, which performs the model order reduction process.\n",
    "2. A module such as `Database`, where the matrices of snapshots and parameters are stored. \n",
    "3. A dimensionality reduction method such as Proper Orthogonal Decomposition `POD` or Auto-Encoder network `AE`.\n",
    "4. An interpolation method to obtain an approximation for the parametric solution for a new set of parameters such as the Radial Basis Function `RBF`, Gaussian Process Regression `GPR`,  K-Neighbors Regressor `KNeighborsRegressor`,  Radius Neighbors Regressor `RadiusNeighborsRegressor` or Multidimensional Linear Interpolator `Linear`.\n",
    "\n",
    "We also need to import:\n",
    "* `numpy:` to handle arrays and matrices we will be working with.\n",
    "* `torch:` to enable the usage of Neural Networks\n",
    "* `matplotlib.pyplot:` to handle the plotting environment. \n",
    "* `matplotlib.tri:` for plotting of the triangular grid."
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "533010c9",
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   "source": [
    "# Database module\n",
    "from ezyrb import Database\n",
    "\n",
    "# Dimensionality reduction methods\n",
    "from ezyrb import POD, AE\n",
    "\n",
    "# Approximation/interpolation methods\n",
    "from ezyrb import RBF, GPR, KNeighborsRegressor, RadiusNeighborsRegressor, Linear, ANN\n",
    "\n",
    "# Model order reduction calss\n",
    "from ezyrb import ReducedOrderModel as ROM\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "import matplotlib.tri as mtri\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", message=\"Ill-conditioned matrix \")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1004e3f8",
   "metadata": {},
   "source": [
    "Before starting with the reduced order model, we visualize some of the snapshots in our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "95b5d41e",
   "metadata": {
    "scrolled": false
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\n",
      "text/plain": [
       "<Figure size 1152x576 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=3, ncols=3, figsize=(16, 8), sharey=True, sharex=True)\n",
    "ax = ax.flatten()\n",
    "for i in range(9):\n",
    "    ax[i].tricontourf(data.triang, data.snapshots['vx'][i], levels=16)\n",
    "    ax[i].set_title('Original snapshot at inlet velocity = {}'.format(*data.params[i].round(2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8eaf8f0a",
   "metadata": {},
   "source": [
    "In this step, we perform the model order reduction to obtain a reduced space from the full order space. We refer to [Tutorial 1](https://github.com/mathLab/EZyRB/blob/master/tutorials/tutorial-1.ipynb) for the description of the basic workflow, here we just quickly describe the steps implemented in the next cell.\n",
    "\n",
    "We start by passing the matrices of the parameters and snapshots to the `Database()` class. It must be said that at this time we create the ROM for the `vx` field. We also instantiate the `POD` and `RBF` object to have a benchmark ROM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4d34d552",
   "metadata": {},
   "outputs": [],
   "source": [
    "db = Database(data.params, data.snapshots['vx'])\n",
    "rom = ROM(db, POD(), RBF())\n",
    "rom.fit();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebfae4bf",
   "metadata": {},
   "source": [
    "Three lines for a data-driven reduced order model, not bad!\n",
    "\n",
    "Just to have a visual check that everything is going well, we plot the approximation for new parameters in the range $[1, 80]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5fcfaef2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_params = np.random.uniform(size=(2))*79.+1.\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 3))\n",
    "for i, param in enumerate(new_params):\n",
    "    ax[i].tricontourf(data.triang, *rom.predict([param]).snapshots_matrix)\n",
    "    ax[i].set_title('Predicted snapshots at inlet velocity = {}'.format(param))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b7be444",
   "metadata": {},
   "source": [
    "We are now calculating the approximation error to see how close is our reduced solution to the full-order solution/simulation using the **k-fold Cross-Validation** strategy by passing the number of splits to the `ReducedOrderModel.kfold_cv_error(n_splits)` method, which operates as follows: \n",
    "\n",
    "1. Split the dataset (parameters/snapshots) into $k$-number of groups/folds.\n",
    "2. Use $k-1$ groups to calculate the reduced space and leave one group for testing.\n",
    "3. Use the approximation/interpolation method to predict each snapshot in the testing group.\n",
    "4. Calculate the error for each snapshot in the testing group by taking the difference between the predicted and the original snapshot. \n",
    "5. Average the errors for predicting snapshots of the testing group/fold.\n",
    "6. Repeat this procedure using different groups for testing and the remaining $k-1$ groups to calculate the reduced space.\n",
    "7. In the end, we will have $k$-number errors for predicting each group/fold that we can average them to have one value for the error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f9f4483c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average error for each fold:\n",
      "   4.955806193579243e-06\n",
      "   2.7585123665319248e-05\n",
      "   6.53585757525929e-05\n",
      "   8.07049318271821e-05\n",
      "   1.9926312885873252e-06\n",
      "\n",
      "Average error = 3.611941374545217e-05\n"
     ]
    }
   ],
   "source": [
    "errors = rom.kfold_cv_error(n_splits = 5)\n",
    "print('Average error for each fold:')\n",
    "for e in errors:\n",
    "    print('  ',e)\n",
    "print('\\nAverage error = {}'.format(errors.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfa43316",
   "metadata": {},
   "source": [
    "Another strategy for calculating the approximation error is called **leave-one-out** by using the  `ReducedOrderModel.loo_error()` method, which is similar to setting the number of folds equal to the number of snapshots (eg. in this case setting `n_splits` = 500) and it operates as follows:\n",
    "1. Combine all the snapshots except one.\n",
    "2. Calculate the reduced space.\n",
    "3. Use the approximation/interpolation method to predict the removed snapshot.\n",
    "4. Calculate the error by taking the difference between the predicted snapshot and the original removed one.\n",
    "5. The error vector is obtained by repeating this procedure for each snapshot in the database.\n",
    "\n",
    "It is worth mentioning that it consumes more time because we have 500 snapshots and the algorithm will perform space order reduction and calculate the approximation error 500 times. For this reason, we commented the next line of code, in order to limit the computational effort needed to run this tutorial. Uncomment it only if you are a really brave person!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "df343c05",
   "metadata": {},
   "outputs": [],
   "source": [
    "# errors = rom.loo_error()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "945a52e3",
   "metadata": {},
   "source": [
    "### Comparison between different methods\n",
    "\n",
    "One of the advantages of the data-driven reduced order modeling is the modular nature of the method. Practically speaking, we need\n",
    "- a method for reducing the dimensionality of input snapshots;\n",
    "- a method for approximate the solution manifold;\n",
    "\n",
    "allowing in principle a large variety of combinations.\n",
    "\n",
    "The list of implemented **reduction methods** in EZyRB contains: \n",
    "- `POD`: *proper orthogonal decomposition*\n",
    "- `AE`: *autoencoder*\n",
    "\n",
    "while the list of implemented **approximation methods** contains:\n",
    "- `RBF`: *radial basis function interpolation*\n",
    "- `GPR`: *gaussian process regression*\n",
    "- `KNeighborsRegressor`: *k-neighbors regression*\n",
    "- `RadiusNeighborsRegressor`: *radius neighbors regression*\n",
    "- `Linear`: *multidimensional linear interpolation*\n",
    "\n",
    "Moreover, new state-of-the-art methods will arrive, so we invite you to read the [documentation](https://mathlab.github.io/EZyRB/) for the complete list of all the possibilities!\n",
    "\n",
    "In the next cell, we create two dictionaries with the objects, such that we can easily test everything with simple `for` cycles. **WARNING** since several methods require the solution of an optimization problem (eg. GPR, ANN, AE), the cell may require some minutes to be run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2760dcea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                       RBF             GPR      KNeighbors RadiusNeighbors             ANN\n",
      "POD           4.214594e-05    1.123213e-05    8.032581e-03    1.091257e-02    9.259920e-01\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " /u/n/ndemo/.local/lib/python3.6/site-packages/GPy/kern/src/rbf.py:52: RuntimeWarning:overflow encountered in square\n",
      " /u/n/ndemo/.local/lib/python3.6/site-packages/GPy/kern/src/stationary.py:168: RuntimeWarning:overflow encountered in true_divide\n",
      " /u/n/ndemo/.local/lib/python3.6/site-packages/GPy/kern/src/rbf.py:76: RuntimeWarning:invalid value encountered in multiply\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AE            1.982617e+00    1.982617e+00    1.982617e+00    1.982617e+00    1.982611e+00\n"
     ]
    }
   ],
   "source": [
    "reductions = {\n",
    "    'POD': POD('svd',rank=10),\n",
    "    'AE': AE([200, 100, 10], [10, 100, 200], nn.Tanh(), nn.Tanh(), 10),\n",
    "}\n",
    "\n",
    "approximations = {\n",
    "#    'Linear': Linear(),\n",
    "    'RBF': RBF(),\n",
    "    'GPR': GPR(),\n",
    "    'KNeighbors': KNeighborsRegressor(),\n",
    "    'RadiusNeighbors':  RadiusNeighborsRegressor(),\n",
    "    'ANN': ANN([20, 20], nn.Tanh(), 10),\n",
    "}\n",
    "\n",
    "header = '{:10s}'.format('')\n",
    "for name in approximations:\n",
    "    header += ' {:>15s}'.format(name)\n",
    "\n",
    "print(header)\n",
    "for redname, redclass in reductions.items():\n",
    "    row = '{:10s}'.format(redname)    \n",
    "    for approxname, approxclass in approximations.items():\n",
    "        rom = ROM(db, redclass, approxclass)\n",
    "        rom.fit()\n",
    "        row += ' {:15e}'.format(rom.kfold_cv_error(n_splits=5).mean())\n",
    "    \n",
    "    print(row)\n"
   ]
  },
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   "id": "5d055510",
   "metadata": {},
   "source": [
    "In a very compact way, we tested several frameworks - like POD-RBF, POD-GPR, POD-NN -, showing the accuracy reached by any of them.\n",
    "\n",
    "We can also note that the frameworks that involve neural networks (`AE` and `ANN`) show a very poor precision. This is due to the fact of the limited number of epochs we impose in the learning procedure. You can try to increase the number of epochs as we shown in the next cell in order to obtain better results, at the cost of a longer training phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a5353ea6",
   "metadata": {},
   "outputs": [],
   "source": [
    "reductions['AE'] = AE([100, 10], [10, 100], nn.ReLU(), nn.ReLU(), 30000)\n",
    "approximations['ANN'] = ANN([50, 10], nn.ReLU(), 30000)"
   ]
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