docs/examples/pyaudi/Example 2 - PyAudi - Differential Intelligence - Vectorised Duals.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Differential Intelligence - Vectorised Duals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(original by Dario Izzo - extended by Ekin Ozturk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we show the use of `desolver` and vectorised gduals for the numerical integration of multiple initial conditions following the notebook example here [differential intelligence](https://darioizzo.github.io/audi/notebooks/example10.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Stuff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "PyAudi backend is available.\n",
      "Using numpy backend\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "import os\n",
    "import numpy as np\n",
    "\n",
    "os.environ['DES_BACKEND'] = 'numpy'\n",
    "import desolver as de\n",
    "import desolver.backend as D\n",
    "\n",
    "D.set_float_fmt('gdual_vdouble')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Controller representation and “simulator”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take as an example the task of learning a robotic controller. In neuro evolution (or Evolutionary Robotics), the controller is typically represented by a neural network, but for the purpose of explaining this new learning concept we will use a polinomial representation for the controller. Later, changing the controller into a NN with weights as parameters will not change the essence of what is done here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of the controller in terms of some weights parameters\n",
    "def u(state, weights):\n",
    "    x,v = state\n",
    "    a,b,c,e,f,g = weights\n",
    "    return a + b*x + c*v + e*x*v + f*x**2 + g*v**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of the equation of motion (our physics simulator propagating the system to its next state)\n",
    "def eom(state, weights):\n",
    "    x,v = state\n",
    "    dx = v\n",
    "    dv = u(state, weights)\n",
    "    return (dx, dv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical Integration - Runge-Kutta 45 Cash-Karp Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Evolutionary Robotics, Euler propagators are commonly used, but we would like to use a higher order integration scheme that is adaptive in order to minimise computation, and increase the accuracy and precision of the results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are using `gdual_vdouble` in order to integrate multiple initial states simultaneously without any significant loss of computation time due to the very efficient vectorisation of `gdual_vdouble` computations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_different_integrations = 16\n",
    "weights = D.array([D.gdual_vdouble([0.2*(np.random.uniform()-0.5)]*num_different_integrations, _, 4) for _ in \"abcefg\"])\n",
    "x = [D.gdual_vdouble([2.*(np.random.uniform()-0.5) for i in range(num_different_integrations)])]\n",
    "v = [D.gdual_vdouble([2.*(np.random.uniform()-0.5) for i in range(num_different_integrations)])]\n",
    "y0 = D.array(x + v, dtype=D.gdual_vdouble)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rhs(t, state, weights, **kwargs):\n",
    "    return D.array(eom(state, weights))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We integrate the system using the Runge-Kutta-Cash-Karp scheme as the numerical integration system with a dense output computed using a piecewise C1 Hermite interpolating spline. \n",
    "\n",
    "This particular interpolator is used as it satisfies not only the state boundary conditions, but also the gradients and is well suited for approximating the solution continuously up to first order in time.\n",
    "\n",
    "Note that the entire integration is done using gduals and thus the solution and the interpolating spline stored in the OdeSystem instance, `pyaudi_integration`, contains all the information about how the state reached by our robot changes when we change the control weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fba2126d4c004a0dba0b7b4883187e6b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=9000000000.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# We restrict the integration time due to the fact that the controller \n",
    "# is quadratic in the state and causes the state to grow very rapidly.\n",
    "\n",
    "pyaudi_integration = de.OdeSystem(rhs, y0=y0, dense_output=True, t=(0, 3.), dt=0.1, rtol=1e-12, atol=1e-12, constants=dict(weights=weights))\n",
    "\n",
    "pyaudi_integration.set_method(\"RK45\")\n",
    "pyaudi_integration.integrate(eta=True)\n",
    "\n",
    "x,v = pyaudi_integration.sol(D.linspace(0, 1, 20)).T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We numerically integrate 16 initial states and see the paths they follow based on the controller we have defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for _x, _v in zip(D.to_float(x).T, D.to_float(v).T):\n",
    "    plt.plot(_x, _v, 'k')\n",
    "plt.plot(x[0].constant_cf, v[0].constant_cf, 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "xf, vf = x[-1], v[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial xf: [-0.3557066099106508, 0.44343882132762114, -0.8737317576067235, -0.2617441190669201, -0.8796623090368102, 0.3814675250018374, 0.4496686004618328, -0.13184594443243638, -0.8531865179643819, 0.6296049480439482, 1.272489314100466, -0.37367300287583055, 0.21369263660756216, -0.4685920682632495, 0.12662167090356946, 1.7123448444138816]\n",
      "initial vf: [0.5118610410272438, -0.3701236243745896, -0.5532466100960509, -0.6008338241266351, -0.16869925311896916, 1.0191355842763685, 0.03313073890800292, 0.47769851923104645, -0.8193041150168822, 0.12783245934453705, 0.8664324532172547, -0.8819129622656402, -0.5007364437236071, 0.00378088557268934, -0.36570546484320804, 0.8206755520959318]\n"
     ]
    }
   ],
   "source": [
    "print(\"initial xf: {}\".format(xf.constant_cf))\n",
    "print(\"initial vf: {}\".format(vf.constant_cf))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Studying the effects of the weights on the behavior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have represented all the robot behavior (x, v) as a polynomial function of the weights. So we now know what happens to the behaviour if we change the weights!! Lets see … we only consider the final state, but the same can be done for all states before.\n",
    "\n",
    "Furthermore, we can compute this for all the different initial states that we integrated thus finding out how the final state of the robot changes for multiple initial conditions. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "new xf: [-0.3644798190145982, 0.447495385967943, -0.8648361515237677, -0.2592939994695151, -0.8727114343058243, 0.3628173608150842, 0.4511668988597944, -0.14014616132168833, -0.8452539766438874, 0.632267395802166, 1.2758792802868362, -0.3718043764184628, 0.21623106958504587, -0.4679969881995721, 0.12859034018369273, 1.7319060943023437]\n",
      "new vf: [0.4936346648964618, -0.36314723947811245, -0.5327100009566508, -0.5946732215257815, -0.15413715024294478, 0.9842045102773821, 0.0361826243667708, 0.4608953840430959, -0.7987016506520095, 0.13376814463127482, 0.8819766632015573, -0.8750423106238954, -0.49627765398605556, 0.004878367143968462, -0.36209906157800886, 0.8727946071182053]\n"
     ]
    }
   ],
   "source": [
    "dweights = dict({'da': -0.002, 'db': 0.003, 'dc': -0.02, 'de': 0.03, 'df': 0.02, 'dg': -0.01})\n",
    "#Lets predict the new final position of our 'robot' if we change his controller as defined above\n",
    "print(\"new xf: {}\".format(xf.evaluate(dweights)))\n",
    "print(\"new vf: {}\".format(vf.evaluate(dweights)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check that we learned the correct map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now simulate again our behavior using the new weights to see where we end up to check if the prediction made after our differential learning is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_weights = D.array([it + dweights['d' + it.symbol_set[0]] for it in weights])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9a515a8558cd433bbc4fec3da6afe7ba",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=9000000000.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "pyaudi_integration2 = de.OdeSystem(rhs, y0=y0, dense_output=True, t=(pyaudi_integration.t[0], pyaudi_integration.t[-1]), dt=0.1, rtol=1e-12, atol=1e-12, constants=dict(weights=new_weights))\n",
    "\n",
    "pyaudi_integration2.set_method(\"RK45\")\n",
    "pyaudi_integration2.integrate(eta=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16,16))\n",
    "x2, v2 = pyaudi_integration2.sol(D.linspace(0, 1, 20)).T\n",
    "for idx, (_x, _v) in enumerate(zip(D.to_float(x).T, D.to_float(v).T)):\n",
    "    if idx == 0:\n",
    "        plt.plot(_x,_v,'C0',label='original')\n",
    "    else:\n",
    "        plt.plot(_x,_v,'C0')\n",
    "for idx, (_x, _v) in enumerate(zip(D.to_float(x2).T, D.to_float(v2).T)):\n",
    "    if idx == 0:\n",
    "        plt.plot(_x,_v,'C1',label='simulation')\n",
    "    else:\n",
    "        plt.plot(_x,_v,'C1')\n",
    "for idx, (_x, _v) in enumerate(zip(D.array([it.evaluate(dweights) for it in x]).T,D.array([it.evaluate(dweights) for it in v]).T)):\n",
    "    if idx == 0:\n",
    "        plt.plot(_x,_v,'C2+', markersize=8.,label='differential learning')\n",
    "    else:\n",
    "        plt.plot(_x,_v,'C2+', markersize=8.)\n",
    "# plt.plot(x[0].constant_cf, v[0].constant_cf, 'ro')\n",
    "plt.legend(loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we have integrated multiple trajectories, printing all the final states and comparing it to the evaluated polynomial is visually difficult to parse. Instead, we look at the maximum and mean absolute differences between the numerical integration and the map evaluated with the new weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum Absolute Difference xf:\t3.121884417645049e-10\n",
      "Mean Absolute Difference xf:   \t4.664606374771285e-11\n",
      "\n",
      "Maximum Absolute Difference vf:\t9.84426262728988e-10\n",
      "Mean Absolute Difference vf:   \t1.7914556643683355e-10\n"
     ]
    }
   ],
   "source": [
    "print(\"Maximum Absolute Difference xf:\\t{}\".format(D.max(D.abs(D.to_float(x2[-1]) - D.to_float(x[-1].evaluate(dweights))))))\n",
    "print(\"Mean Absolute Difference xf:   \\t{}\".format(D.mean(D.abs(D.to_float(x2[-1]) - D.to_float(x[-1].evaluate(dweights))))))\n",
    "print()\n",
    "print(\"Maximum Absolute Difference vf:\\t{}\".format(D.max(D.abs(D.to_float(v2[-1]) - D.to_float(v[-1].evaluate(dweights))))))\n",
    "print(\"Mean Absolute Difference vf:   \\t{}\".format(D.mean(D.abs(D.to_float(v2[-1]) - D.to_float(v[-1].evaluate(dweights))))))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:python3.7]",
   "language": "python",
   "name": "conda-env-python3.7-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}