docs/examples/pyaudi/Example 1 - PyAudi - Differential Intelligence.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Differential Intelligence"
   ]
  },
  {
   "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` for numerical integration 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_double')"
   ]
  },
  {
   "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": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = D.array([D.gdual_double(0.05*(np.random.uniform()-0.5), _, 7) for _ in \"abcefg\"])\n",
    "x = [D.gdual_double(2*(np.random.uniform()-0.5))]\n",
    "v = [D.gdual_double(2*(np.random.uniform()-0.5))]\n",
    "y0 = D.array(x + v, dtype=D.gdual_double)"
   ]
  },
  {
   "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": "46c915196f6346c6a2310050eaab7da4",
       "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_integration = de.OdeSystem(rhs, y0=y0, dense_output=False, t=(0, 10.), 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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,v = pyaudi_integration.y.T\n",
    "plt.plot([it for it in x.astype(np.float64)],[it for it in v.astype(np.float64)])\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: -0.9571855514218823\n",
      "initial vf: 0.0740202404341646\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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "new xf: -0.5706108199421452\n",
      "new vf: 0.11647309216431377\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 = np.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": "1151e1e3c313464c8ff86d9136f8191c",
       "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=(0, 10.), dt=0.01, 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": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "x2, v2 = pyaudi_integration2.y.T\n",
    "plt.plot([it.constant_cf for it in x],[it.constant_cf for it in v],label='original')\n",
    "plt.plot([it.constant_cf for it in x2],[it.constant_cf for it in v2],'r',label='simulation')\n",
    "plt.plot([it.evaluate(dweights) for it in x],[it.evaluate(dweights) for it in v],'g',label='differential learning')\n",
    "plt.plot(x[0].constant_cf, v[0].constant_cf, 'ro')\n",
    "plt.legend(loc=2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Differential learning xf: \t-0.5706108199421452\n",
      "Real xf: \t\t\t-0.5708065322492378\n",
      "Mean Absolute Difference xf:\t0.00019571230709258813\n",
      "\n",
      "Differential learning vf: \t0.11647309216431377\n",
      "Real vf: \t\t\t0.11620694228805205\n",
      "Mean Absolute Difference vf:\t0.00026614987626172315\n"
     ]
    }
   ],
   "source": [
    "print(\"Differential learning xf: \\t{}\".format(x[-1].evaluate(dweights)))\n",
    "print(\"Real xf: \\t\\t\\t{}\".format(x2[-1].constant_cf))\n",
    "print(\"Mean Absolute Difference xf:\\t{}\".format(D.max(D.abs(D.to_float(x2[-1]) - D.to_float(x[-1].evaluate(dweights))))))\n",
    "print()\n",
    "print(\"Differential learning vf: \\t{}\".format(v[-1].evaluate(dweights)))\n",
    "print(\"Real vf: \\t\\t\\t{}\".format(v2[-1].constant_cf))\n",
    "print(\"Mean Absolute Difference vf:\\t{}\".format(D.max(D.abs(D.to_float(v2[-1]) - D.to_float(v[-1].evaluate(dweights))))))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:desolver]",
   "language": "python",
   "name": "conda-env-desolver-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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}