HO_analytic_derivatives.ipynb

{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
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   "source": [
    "<a href=\"https://colab.research.google.com/github/coreyjadams/AI4NP_School/blob/main/HO_analytic_derivatives.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lyYZggEgoZ8F"
   },
   "source": [
    "Here we compute the ground-state of the $ndim$-dimensional quantum harmonic oscillator for a system of $npart$ particles. The Hamiltonian of the system reads:\n",
    "\n",
    "$$ H = -\\frac{1}{2m} \\sum_{i=1}^{npart} \\vec{\\nabla}_i^2 + \\frac{m \\omega^2}{2}\\sum_{i=1}^{npart} \\vec{x}_i^2 $$\n",
    "\n",
    "For simplicity, we take $m=1$ and $\\omega=1$. According to the variational principle of quantum mechanics, for any trial wave function $|\\psi_T\\rangle$,\n",
    "\n",
    "$$ \\langle \\psi_T | H | \\psi_T \\rangle ~ \\ge ~ E_0 = \\frac{1}{2} ndim * npart $$\n",
    "\n",
    "In this notebook, we assume a trial wave function of the exponential form\n",
    "\n",
    "$$ \\langle x | \\psi_T \\rangle = \\psi_T(x) = \\exp \\left(-\\alpha \\sum_{i=1}^{npart} \\vec{x}_i^2 \\right)$$\n",
    "where the exact ground state is recovered for $\\alpha = 1/2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "rQBcqnMKoIln"
   },
   "outputs": [],
   "source": [
    "# Load the libraries that we need for this notebook\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.gridspec as gridspec\n",
    "from IPython.display import display, clear_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "iy-zay5cxKkf"
   },
   "outputs": [],
   "source": [
    "class Wavefunction(object):\n",
    "    \"\"\"Create a simple wave function in ndim dimensions \n",
    "       and for npart particles\n",
    "       psi(x) = exp(- alpha * sum_i x_i^2)\n",
    "    \"\"\"\n",
    "    def __init__(self, ndim : int, npart : int):\n",
    "        self.ndim = ndim\n",
    "        self.npart = npart\n",
    "\n",
    "    def call(self, alpha, inputs):\n",
    "        psi = - alpha * np.sum(inputs**2, axis=(1,2))\n",
    "        return psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "SCUY_gYb7cbv"
   },
   "outputs": [],
   "source": [
    "class Hamiltonian(object):\n",
    "    \"\"\"Expectation values of the kinetic and potential energies of \n",
    "       a collection of independent harmonic oscillators.\n",
    "    \"\"\"\n",
    "    def __init__(self, ndim : int, npart : int, wavefunction : callable):\n",
    "       self.ndim = ndim\n",
    "       self.npart = npart\n",
    "       self.wavefunction = wavefunction\n",
    "\n",
    "    def potential (self, x):\n",
    "        \"\"\" The HO oscillator potential is given by \n",
    "        V = <x|V|psi> / <x|psi> = 1/2 sum_i x_i^2\n",
    "        \"\"\"\n",
    "        pe = 0.5 * np.sum(x**2, axis=(1,2))\n",
    "        return pe\n",
    "\n",
    "    def kinetic (self, alpha, x):\n",
    "        \"\"\" For the simple wave function that we consider \n",
    "        psi(x) = exp(- alpha * sum_i x_i^2), the kinetic \n",
    "        energy can be computed analytically:  \n",
    "        T = <x|T|psi> / <x|psi> = 1/2 \\sum_i (2 alpha - 4 * alpha**2 * x_i^2 )\n",
    "          = \\sum_i (alpha - 2 * alpha**2 * x_i^2 )\n",
    "        \"\"\"\n",
    "        ke = np.sum( alpha * np.ones_like(x) - 2 * alpha**2 * x**2, axis=(1,2))\n",
    "        return ke\n",
    "\n",
    "    def energy (self, alpha, inputs):\n",
    "        \"\"\" Sum of the kinetic and the potential energy \"\"\"\n",
    "        ke = self.kinetic(alpha, inputs)\n",
    "        pe = self.potential(inputs)\n",
    "        en = ke + pe\n",
    "        return ke, pe, en"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "ReqTewSvKKue"
   },
   "outputs": [],
   "source": [
    "class Metropolis(object):\n",
    "    \"\"\"Metropolis Sampler in N dimension\n",
    "\n",
    "    Sample from N-D coordinates, using some initial probability distribution\n",
    "\n",
    "    \"\"\"\n",
    "    def __init__(self,   \n",
    "          nwalk : int, \n",
    "          npart : int,\n",
    "          ndim : int,\n",
    "          neq : int, \n",
    "          nav : int, \n",
    "          nvoid : int, \n",
    "          sig : float,\n",
    "          sig_i : float,\n",
    "          wavefunction : callable):\n",
    "\n",
    "          self.nwalk = nwalk \n",
    "          self.npart = npart\n",
    "          self.ndim = ndim\n",
    "          self.neq = neq\n",
    "          self.nav = nav\n",
    "          self.nvoid = nvoid\n",
    "          self.sig = sig\n",
    "          self.sig_i = sig_i\n",
    "          self.wavefunction = wavefunction\n",
    "\n",
    "# Function that performs nvoid Metropolis steps\n",
    "    def step(self, alpha, x_o):\n",
    "        for i in range(self.nvoid):\n",
    "            log_wpsi_o = self.wavefunction.call(alpha, x_o)\n",
    "            x_n = x_o + self.sig * np.random.normal(size=[self.nwalk, self.npart, self.ndim])\n",
    "            log_wpsi_n = self.wavefunction.call(alpha, x_n)\n",
    "            prob = np.exp( 2 * ( log_wpsi_n - log_wpsi_o ) )\n",
    "            accept = np.greater(prob, np.random.uniform(size=[self.nwalk]))\n",
    "            x_o = np.where(accept.reshape([self.nwalk,1,1]), x_n, x_o)\n",
    "            acc_o = accept.astype('float64')\n",
    "        return x_o, acc_o\n",
    "\n",
    "# Function that perform the full Metropolis walk and returns the path and the acceptance\n",
    "    def walk(self, alpha):\n",
    "        x_o = self.sig_i * np.random.normal(size=[self.nwalk, self.npart, self.ndim])\n",
    "        for i in range (neq): \n",
    "            x_o, acc_o = self.step(alpha, x_o)\n",
    "        x_s = []\n",
    "        acc_s = []\n",
    "        for i in range (self.nav): \n",
    "            x_o, acc_o = self.step(alpha, x_o)\n",
    "            x_s.append(x_o)\n",
    "            acc_s.append(acc_o)\n",
    "        x_s = np.concatenate(x_s)\n",
    "        acc_s = np.concatenate(acc_s)\n",
    "        return x_s, acc_s "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "N1z8mRn0bPYl"
   },
   "outputs": [],
   "source": [
    "# Define the function that computes the average and the standard deviation of each observables\n",
    "def estimator(observable):\n",
    "    average = np.mean(observable)\n",
    "    average_2 = np.mean(observable**2)\n",
    "    error = np.sqrt(average_2 - average**2) / np.sqrt(observable.shape[0]-1) \n",
    "    return average, error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "cvaeAdMhG1g6"
   },
   "outputs": [],
   "source": [
    "# Set the parameters and instanciate the Wavefunction, Hamiltonian, and Metropolis classes \n",
    "sig_i = 1.0         # Gaussian width for sampling the initial configuration \n",
    "sig = 0.2           # Gaussian width for sampling the Metropolis Move\n",
    "neq = 20            # Equilibration steps\n",
    "nav = 2             # Averaging steps\n",
    "nvoid = 200         # Void steps between energy calculations\n",
    "nwalk = 100         # Quantum Monte Carlo configurations\n",
    "ndim = 3            # Spatial dimension  \n",
    "npart = 2           # Number of particles\n",
    "seed = 19.          # Seed to initialize the random-number generator\n",
    "alpha = 0.6         # Gaussian width of the HO wave function \n",
    "\n",
    "wavefunction = Wavefunction(ndim, npart)\n",
    "hamiltonian = Hamiltonian(ndim, npart, wavefunction)\n",
    "metropolis = Metropolis(nwalk, npart, ndim, neq, nav, nvoid, sig, sig_i, wavefunction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ditWt9kBUSmy",
    "outputId": "fe28e578-2327-4b6a-ed0b-cf3f4a41d6da"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy = 3.045 +- 0.022\n",
      "kinetic energy = 1.783 +- 0.071\n",
      "potential energy = 1.262 +- 0.049\n"
     ]
    }
   ],
   "source": [
    "# Compute the expectation values by doing a Metropolis walk \n",
    "x_s, acc_s = metropolis.walk(alpha)\n",
    "ke, pe, en =  hamiltonian.energy(alpha, x_s)\n",
    "\n",
    "energy_average, energy_error = estimator(en)\n",
    "kinetic_average, kinetic_error = estimator(ke)\n",
    "potential_average, potential_error = estimator(pe)\n",
    "print(f\"energy = {energy_average:.3f} +- {energy_error:.3f}\")\n",
    "print(f\"kinetic energy = {kinetic_average:.3f} +- {kinetic_error:.3f}\")\n",
    "print(f\"potential energy = {potential_average:.3f} +- {potential_error:.3f}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "cXapIdjBbWKI"
   },
   "outputs": [],
   "source": [
    "class Optimizer(object):\n",
    "    \"\"\"Class that computes the energy derivative \n",
    "    f_i = 2[< E_L O_i > - 2 < E_L > < O_i >]\n",
    "    and updates the parameters according to the SGD algorithm\n",
    "    \"\"\"\n",
    "    def __init__(self, ndim : int, npart : int, wavefunction : callable):\n",
    "       self.ndim = ndim\n",
    "       self.npart = npart\n",
    "       self.wavefunction = wavefunction\n",
    "\n",
    "# Computes the derivative of the wave function O_i\n",
    "    def jacobian (self, x):\n",
    "        jac = - np.sum(x**2, axis=(1,2))\n",
    "        return jac\n",
    "\n",
    "# Computes the gradient of the energy f_i = 2[ < E_L O_i > - 2 < E_L > < O_i > ]\n",
    "    def gradient (self, x, en):\n",
    "        jac = self.jacobian(x)\n",
    "        grad_energy = 2 * (np.mean(en * jac) - np.mean(en) * np.mean(jac))\n",
    "        return grad_energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jj8tV4hCIkIy",
    "outputId": "d2cdf139-e059-4eb6-ea80-6532b7517937"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy = 3.000 +- 0.000\n",
      "kinetic energy = 1.551 +- 0.058\n",
      "potential energy = 1.449 +- 0.058\n",
      "energy gradient= 0.00000\n"
     ]
    }
   ],
   "source": [
    "# Compute the expectation values and the derivative of the energy \n",
    "alpha = 0.5\n",
    "optimizer = Optimizer(ndim, npart, wavefunction) \n",
    "x_s, acc_s = metropolis.walk(alpha)\n",
    "ke, pe, en =  hamiltonian.energy(alpha, x_s)\n",
    "\n",
    "energy_average, energy_error = estimator(en)\n",
    "kinetic_average, kinetic_error = estimator(ke)\n",
    "potential_average, potential_error = estimator(pe)\n",
    "energy_gradient = optimizer.gradient(x_s, en)\n",
    "print(f\"energy = {energy_average:.3f} +- {energy_error:.3f}\")\n",
    "print(f\"kinetic energy = {kinetic_average:.3f} +- {kinetic_error:.3f}\")\n",
    "print(f\"potential energy = {potential_average:.3f} +- {potential_error:.3f}\")\n",
    "\n",
    "print(f\"energy gradient= {energy_gradient:.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 537
    },
    "id": "YmlSycs7M7yk",
    "outputId": "43eec6ba-2bde-4ad9-c248-904c955e8de5"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x648 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Optimize with the simple SGD algorithm \n",
    "alpha = 1.2\n",
    "LR = 0.002\n",
    "\n",
    "# Define a figure here which we can update along the way:\n",
    "fig       = plt.figure(figsize=(16,9))\n",
    "# Create 2x2 sub plots\n",
    "\n",
    "gs = gridspec.GridSpec(2, 2)\n",
    "ax_loss   = plt.subplot(gs[:,0])\n",
    "ax_err    = plt.subplot(gs[:,1])\n",
    "\n",
    "steps_history = []\n",
    "energy_history  = []\n",
    "error_history = []\n",
    "for i in range (400):\n",
    "    x_s, acc_s = metropolis.walk(alpha)\n",
    "    ke, pe, en =  hamiltonian.energy(alpha, x_s) \n",
    "    energy_average, energy_error = estimator(en)\n",
    "    energy_gradient = optimizer.gradient(x_s, en)\n",
    "    alpha = alpha - LR * energy_gradient\n",
    "\n",
    "    steps_history.append(i)\n",
    "    energy_history.append(energy_average)\n",
    "    error_history.append(energy_error)\n",
    "\n",
    "    # Here we update the plots.  Show the energy function:\n",
    "    ax_loss.set_xlim(0, 1.1*i)\n",
    "    ax_loss.cla()\n",
    "    ax_loss.plot(steps_history, energy_history, label=\"Energy\")\n",
    "    ax_loss.grid(True)\n",
    "    ax_loss.legend(fontsize=25)\n",
    "\n",
    "    # Show the error function:\n",
    "    ax_err.set_xlim(0, 1.1*i)\n",
    "    ax_err.cla()\n",
    "    ax_err.plot(steps_history, error_history, label=\"Error\")\n",
    "    ax_err.grid(True)\n",
    "    ax_err.legend(fontsize=25)\n",
    "\n",
    "    display(fig)\n",
    "    clear_output(wait = True)\n",
    "    plt.pause(0.25)\n",
    "    \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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