{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Using machine learning in cosmology, astronomy and physics\n",
    "\n",
    "Tom Charnock\n",
    "\n",
    "Institut d'Astrophysique de Paris\n",
    "<br><br>\n",
    "Slides available at [presentations.charnock.fr/ML_cosmo_astro_physics](http://presentations.charnock.fr/ML_cosmo_astro_physics)\n",
    "\n",
    "<div class=\"row\">\n",
    "    <div style=\"float: left; width: 20%; padding-right: 70px; padding-top:20px\">\n",
    "        <img src=\"../figures/SU.png\" alt=\"Sorbonne Université\" style=\"width:80%;\"/>\n",
    "    </div>\n",
    "    <div style=\"float: left; width: 20%; padding: 5px;padding-top:20px\">\n",
    "        <img src=\"../figures/ASU.svg\" alt=\"Alliance Sorbonne Université\" style=\"width:62%;\"/>\n",
    "    </div>\n",
    "    <div style=\"float: left; width: 20%; padding: 5px;\">\n",
    "        <img src=\"../figures/IAP.png\" alt=\"IAP\" style=\"width:40%;\"/>\n",
    "    </div>\n",
    "    <div style=\"float: left; width: 20%; padding: 5px;padding-top:10px\">\n",
    "        <img src=\"../figures/CNRS.png\" alt=\"CNRS\" style=\"width:30%;\"/>\n",
    "    </div>\n",
    "    <div style=\"float: left; width: 20%; padding: 5px;padding-top:10px\">\n",
    "        <img src=\"../figures/Aquila.png\" alt=\"Aquila\" style=\"width:60%;\"/>\n",
    "    </div>\n",
    "</div> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2 style=\"margin-bottom:2%\">Who am I?</h2>\n",
    "\n",
    "<table width=100% style=\"margin-top:0\">\n",
    "    <tr style=\"background:none;font-style:italic;margin-top:0;text-align:center;font-size:1.5em\">\n",
    "        <th style=\"text-align:center\">\n",
    "            Statistician\n",
    "        </th><th style=\"text-align:center\">\n",
    "            Machine learning guru\n",
    "        </th><th style=\"text-align:center\">\n",
    "            Cosmologist\n",
    "        </th>\n",
    "    </tr>\n",
    "</table>\n",
    "<div style=\"float:left;width:100%;margin-top:5%\">\n",
    "    <div style=\"float:left;width:50%\">\n",
    "        <img style=\"display: block;margin: 0 auto;\" width=50% src=\"../figures/me.jpeg\"/>\n",
    "    </div>\n",
    "    <div style=\"float:left;width:50%;margin-top:0\">\n",
    "        <h3 style=\"text-align:right\">What do I work on?</h3>\n",
    "        <h5>\n",
    "            Developing statistical machine learning methods to make safe and understandable models<br><br>\n",
    "            Advising and consulting on how to best extract information<br><br>\n",
    "            Telling people when people are misinterpretting their results\n",
    "        </h5>\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Neural networks using in a Bayesian setting\n",
    "(Charnock, Lavaux, Wandelt, Sarma Boruah, Jasche and Hudson 2020)\n",
    "\n",
    "<div style=\"float:left;width:100%;margin:0 auto;padding-top:5%\">\n",
    "    <div style=\"float:left;width:50%\">\n",
    "        <img width=45% style=\"display: block;margin: 0 auto;\" src=\"../figures/with_NN.svg\"/>\n",
    "    </div>\n",
    "    <div style=\"float:left;width:50%\">\n",
    "        <h5 style=\"padding-top:0;margin-top:-5%\">Inferring cosmological parameters and initial conditions of simulations from noisy (horrible) data</h5>\n",
    "        <ul>\n",
    "            <li>Forward model all understood physics<br></li>\n",
    "            <li>Make abstract function (NN) made from physically motivated architecture choice<br></li>\n",
    "            <li>Use high dimensional Markov methods to sample physical properties AND neural network parameters<br><br></li>\n",
    "        </ul>\n",
    "        <br>\n",
    "        Not deep learning anymore - we're just benefitting from the differentiable frameworks and doing <i>old-school* physics</i> 😉\n",
    "    </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img style=\"width:80%;display:block;height:auto;margin:auto;float:none!important;\" src=\"../figures/BORG.svg\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Why is machine learning essential in cosmology, astrophysics and physics?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### It's really fast! \n",
    "\n",
    "##### Old techniques could take days, weeks or months of processing time (on high performance computing facilities)\n",
    "\n",
    "<img style=\"width:40%;display:block;height:auto;margin:auto;float:none!important;padding-top:2%;margin-bottom:-2em\" src=\"figures/superresolution.png\"/>\n",
    "\n",
    "<h5 style=\"float:left;\">\n",
    "    I can now do in my office in seconds (after training)\n",
    "</h5>\n",
    "<h5 style=\"float:right\">\n",
    "    It's eco-friendly!\n",
    "</h5>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Handling large data volumes\n",
    "\n",
    "<div style=\"float:left;width:50%;margin-top:5%\">\n",
    "    <table>\n",
    "        <tr>\n",
    "            <th>\n",
    "                Sky Survey Projects\t\n",
    "            </th><th>\n",
    "                Data Volume\n",
    "            </th><th>\n",
    "                Year\n",
    "            </th>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                DPOSS (The Palomar Digital Sky Survey)\n",
    "            </td><td>\n",
    "                3 TB\n",
    "            </td><td>\n",
    "                1950s - 1980s\n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                2MASS (The Two Micron All-Sky Survey)\n",
    "            </td><td>\n",
    "                10 TB\n",
    "            </td><td>\n",
    "                1997 - 2001 \n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                GBT (Green Bank Telescope)\n",
    "            </td><td>\n",
    "                20 PB\n",
    "            </td><td>\n",
    "                2001 -\n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                GALEX (The Galaxy Evolution Explorer)\n",
    "            </td><td>\n",
    "                30 PB\n",
    "            </td><td>\n",
    "                2003 - 2013\n",
    "            </td>\n",
    "           </tr><tr>\n",
    "            <td>\n",
    "                SDSS (The Sloan Digital Sky Survey)\n",
    "            </td><td>\n",
    "                40 TB\n",
    "            </td><td>\n",
    "                2000 - 2020\n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                SkyMapper Southern Sky Survey\n",
    "            </td><td>\n",
    "                500 TB\n",
    "            </td><td>\n",
    "                2014 - 2021\n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                PanSTARRS (The Panoramic Survey Telescope and Rapid Response System)\n",
    "            </td><td>\n",
    "                ~ 40 PB expected\n",
    "            </td><td>\n",
    "                2008 -\n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                Vera C. Rubin Observatory<br>\n",
    "                LSST (The Legacy Survey of Space and Time)\n",
    "            </td><td>\n",
    "                ~ 200 PB expected\n",
    "            </td><td>\n",
    "                2021 -\n",
    "            </td>\n",
    "        </tr><tr>\n",
    "            <td>\n",
    "                SKA (The Square Kilometer Array)\n",
    "            </td><td>\n",
    "                ~ 4.6 EB expected\n",
    "            </td><td>\n",
    "                2027 -\n",
    "            </td>\n",
    "        </tr>\n",
    "    </table>\n",
    "</div>\n",
    "<div style=\"float:left;width:50%\">\n",
    "    <br><br>\n",
    "    <img src=\"figures/datavolume.svg\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "survey = [\n",
    "    \"DPOSS\", \n",
    "    \"2MASS\", \n",
    "    \"GBT\", \n",
    "    \"GALEX\", \n",
    "    \"SDSS\", \n",
    "    \"SkyMapper\", \n",
    "    \"PanSTARRS\",\n",
    "    \"LSST\",\n",
    "    \"SKA\"]\n",
    "start = [\n",
    "    1950, \n",
    "    1997, \n",
    "    2001, \n",
    "    2003, \n",
    "    2000, \n",
    "    2014, \n",
    "    2008,\n",
    "    2021,\n",
    "    2028]\n",
    "end = [\n",
    "    1980, \n",
    "    2001, \n",
    "    None, \n",
    "    2013, \n",
    "    2020, \n",
    "    2021, \n",
    "    None,\n",
    "    None,\n",
    "    None]\n",
    "data = [\n",
    "    3*1024**4, \n",
    "    10*1024**4, \n",
    "    20*1024**5, \n",
    "    30*1024**5, \n",
    "    40*1024**4, \n",
    "    500*1024**4, \n",
    "    30*1024**5,\n",
    "    200*1024**5,\n",
    "    4.6*1024**6]\n",
    "\n",
    "with plt.xkcd():\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(10, 8))\n",
    "    for a, b, c, d in zip(survey, start, end, data):\n",
    "        if c is None:\n",
    "            c = 2040\n",
    "        if a == \"PanSTARRS\":\n",
    "            d *= 1.5\n",
    "        ax.semilogy([b, c], [d / (1024**4), d / (1024**4)], label=a, linewidth=5)\n",
    "        \n",
    "    ax.set_ylabel(\"Amount of data (TB)\")\n",
    "    ax.set_xlabel(\"Operational years\")\n",
    "    ax.set_xlim(1950, 2035)\n",
    "    ax.legend(frameon=False)\n",
    "    ax.plot(np.linspace(1950, 2035, 100), 3 * np.exp(np.exp(np.linspace(-3, 3, 100))))\n",
    "    plt.savefig(\"figures/datavolume.svg\", bbox_inches=\"tight\", transparent=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Fit functions when we do not actually know the physics describing what is happening (physics vs data)\n",
    "##### Neural networks - parameterisable functions \\\\(\\mathscr{f}_{w,a}:x\\in\\mathcal{X}\\mapsto y\\in\\mathcal{Y}\\\\)\n",
    "\n",
    "<div style=\"float:left;width:100%;margin:0 auto;text-align:center;\">\n",
    "    <img width=30% style=\"display: inline;margin: 0 auto;\" src=\"../figures/annotated_neural_network.svg\"/>\n",
    "    <img width=40% style=\"display: inline;margin: 0 auto;padding-left:5%;padding-bottom:5%\" src=\"../figures/mapping.svg\"/>\n",
    "    <br><br>\n",
    "    Stacks of non-linear activated weighted sums - \\\\(\\displaystyle n_j^l = \\phi\\left(\\sum_iw_{ji}n^{l-1}_i+b_j\\right)\\\\)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Classifying astrophysical events\n",
    "<div style=\"float:left;width:100%;margin:0 auto;margin-top:5%;\">\n",
    "    <img width=65% style=\"display: block;margin: 0 auto;\" src=\"../figures/FLEET.svg\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Where are people going wrong?\n",
    "\n",
    "<div style=\"float:left;width:50%;margin-top:5%\">\n",
    "    <img width=80% src=\"../figures/nn_b_t.gif\"/>\n",
    "</div>\n",
    "<div style=\"float:left;width:50%;margin-top:5%\">\n",
    "    <h5>Neural networks and deep learning are presented as magical black boxes (they aren't)</h5>\n",
    "    <h5>It is easy to take pretrained ones (and they normally \"work\" suprisingly well without any modifications)</h5>\n",
    "    <h5>A lot of people want quantitative results over qualitative results</h5>   \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### How should we think about neural networks?\n",
    "\n",
    "- Deep learning is really making a probabilistic model for the distribution of data\n",
    "\n",
    "- We can see some observable and we want to describe how and why we see what we have seen.\n",
    "- Using physics we could describe this a bunch of processes, like gravity or other theories\n",
    "- Then we can find out what values of the parameters of the model we have made are given that we have observed some data.\n",
    "- The same is true for a neural network, but now the parameters are the weights and biases of the network and they don't have physical meaning.\n",
    "- People normally ignore this fact and just accept the output of the network as a magical result which can be trusted based on whether it fits other data (this isn't a scientific statement because we need to know how likely any predictions will be correct or not, its just a statement of error - like a human would make)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### How should we think about neural networks?\n",
    "\n",
    "<img style=\"display: block;margin: 0 auto;margin-top:2%\" width=75% src=\"../figures/statistical_model_w.svg\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### How should we think about neural networks?\n",
    "\n",
    "<img style=\"display: block;margin: 0 auto;margin-top:2%\" width=75% src=\"../figures/statistical_network.svg\"/>"
   ]
  },
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   "source": [
    "### We're making models for how likely we are to see data\n",
    "\n",
    "<div style=\"float:left;width:50%;margin-top:5%\">\n",
    "    <img width=80% src=\"../figures/vi_b_t.gif\"/>\n",
    "</div>\n",
    "<div style=\"float:left;width:50%;margin-top:5%\">\n",
    "    <h5>We do not know if the model is a good choice</h5>\n",
    "    <h5>It certainly won't be as good or as interpretable as a physical model</h5><br>\n",
    "    <h5>It's still fast and informative</h5>   \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Machine learning to accelerate science\n",
    "\n",
    "<div style=\"float:left;width:100%;margin:0 auto;margin-top:3%;margin-bottom:3%\">\n",
    "    <img width=50% style=\"display: block;margin: 0 auto;\" src=\"../figures/FLEET.svg\"/>\n",
    "</div>\n",
    "\n",
    "There are many times that we can use machine learning to accelerate the way that we obtain data which we can use for science, rather than using the network itself for science."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Why is machine learning well suited to physics?"
   ]
  },
  {
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   "metadata": {
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    }
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   "source": [
    "### Network architectures (actually doing different physics)"
   ]
  },
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   "metadata": {
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    }
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   "source": [
    "## Convolutional networks\n",
    "<br>\n",
    "\n",
    "<div style=\"float:left;width:100%;margin:0 auto\">\n",
    "    <img width=70% style=\"display: block;margin: 0 auto;\" src=\"../figures/autoencoder_example.svg\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Convolutions\n",
    "<div style=\"float:left;width:100%;margin:0 auto;padding-top:5%;padding-bottom:5%\">\n",
    "    <img width=100% style=\"display: block;margin: 0 auto;\" src=\"../figures/feature_maps_lr_incep_7x7x7_light_7x7x7.svg\"/>\n",
    "</div>\n",
    "\n",
    "##### Translational invariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "### Weight sharing\n",
    "<div style=\"float:left;width:100%;margin:0 auto;padding-top:5%;padding-bottom:5%\">\n",
    "    <img width=45% style=\"display: block;margin: 0 auto;\" src=\"../figures/multipole_kernels.svg\"/>\n",
    "</div>\n",
    "\n",
    "##### Other invariances (rotational, etc.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Residual connections\n",
    "\n",
    "<div style=\"float:left;width:100%;margin:0 auto;padding-top:2%;padding-bottom:5%\">\n",
    "    <img style=\"max-width:80%;max-height:40%;display:block;height:auto;margin:auto;float:none!important;\" src=\"../figures/resnet.svg\">\n",
    "</div> \n",
    "\n",
    "##### Perturbative expansion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Kernel sizes\n",
    "<div style=\"float:left;width:100%;margin:0 auto;padding-top:2%;padding-bottom:5%\">\n",
    "    <div style=\"float:left;width:50%\">\n",
    "    <img style=\"max-width:100%;max-height:60%;display:inline-block;height:auto;margin:auto;float:none!important;\" src=\"../figures/receptive_field.svg\">\n",
    "    </div>\n",
    "    <div style=\"float:left;width:50%\">\n",
    "        <div style=\"float:left;width:100%;margin:0 auto\">\n",
    "            <img width=70% style=\"display: block;margin: 0 auto;\" src=\"../figures/feature_maps_lr_incep_7x7x7_light_3x3x3.svg\"/>\n",
    "        </div>\n",
    "        <div style=\"float:left;width:100%;margin:0 auto\">\n",
    "            <img width=70% style=\"display: block;margin: 0 auto;\" src=\"../figures/feature_maps_lr_incep_7x7x7_light_5x5x5.svg\"/>\n",
    "        </div>\n",
    "        <div style=\"float:left;width:100%;margin:0 auto\">\n",
    "            <img width=70% style=\"display: block;margin: 0 auto;\" src=\"../figures/feature_maps_lr_incep_7x7x7_light_7x7x7.svg\"/>\n",
    "        </div>\n",
    "    </div>\n",
    "</div>\n",
    "\n",
    "##### Causal connections"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Optimised architectures\n",
    "\n",
    "<div style=\"float:left;width:100%;margin:0 auto;padding-top:2%;margin-bottom:5%\">\n",
    "    <div style=\"float:left;width:45%;margin:0 auto\">\n",
    "        <center><h1 style=\"padding-bottom:3%\">U-net</h1></center>\n",
    "        <img style=\"max-width:100%;display:inline-block;height:auto;margin:auto;float:none!important;\" src=\"../figures/U-net.svg\">\n",
    "    </div>\n",
    "    <div style=\"float:left;width:50%;margin:0 auto;\">\n",
    "        <center><h1 style=\"padding-bottom:10%\">Inception</h1></center>\n",
    "        <img style=\"max-width:100%;display:inline-block;height:auto;margin:auto;float:none!important;\" src=\"../figures/Inception.svg\">\n",
    "    </div>\n",
    "</div>\n",
    "\n",
    "\n",
    "\n",
    "##### Scale invariance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "# Conclusions\n",
    "\n",
    "#### Neural networks are very powerful functions - but they make useless predictive scientific models\n",
    "\n",
    "#### They can be used to accelerate and target data collection to be used to improve science\n",
    "\n",
    "#### We can also build properly rigorous statistical frameworks around them<br>(likelihood-free inference) to do good science again"
   ]
  }
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