{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 11.1\n", "## Air-shower reconstruction\n", "Follow the description of a cosmic-ray observatory in Example 11.2 and Fig. 11.2(b).\n", "The simulated data contain 9 × 9 detector stations which record traversing particles from the cosmic-ray induced air shower. \n", "Each station measures two quantities, which are stored in the form of a map (2D array) corresponding to the station positions in offset coordinates:\n", "- arrival time T: time point of detection in seconds\n", "- signal S: signal strength in arbitrary units\n", "\n", "The following shower properties need to be reconstructed:\n", "- axis: x, y, z unit vector of the shower arrival direction\n", "- core: position of the shower core in meters\n", "- logE: $\\log_{10} (E / \\mathrm{eV})$, energy of the cosmic ray\n", "\n", "Reconstruct the properties of the arriving cosmic rays by analyzing their\n", "air showers:\n", "\n", "### Tasks \n", "1. Set up a multi-task regression network for simultaneously predicting shower direction, shower core position, and energy. The network should consist of a common part to the three properties, followed by an individual subnetwork for each property. Combine the mean squared errors of the different properties using weights $w_j$. \n", "\n", "\n", "2. Train the model to the following precisions:\n", "- Better than $1.5^\\circ$ angular resolution\n", "- Better than $25$ m core position resolution\n", "- Better than $10\\%$ relative energy uncertainty $\\left(\\frac{E_\\mathrm{pred} - E_\\mathrm{true}}{E_\\mathrm{true}}\\right)$\n", "\n", " Estimate what these requirements mean in terms of the mean squared error loss and adjust the relative weights in the objective function accordingly. \n", "\n", "3. Plot and interpret the resulting training curves, both with and without the weights $w_j$ in the objective function.\n", "\n", "\n", "##### Hint: using a GPU for this task may be advantageous!" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "keras 2.4.0\n" ] } ], "source": [ "from tensorflow import keras\n", "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "layers = keras.layers\n", "\n", "print(\"keras\", keras.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Download data" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import os\n", "import gdown\n", "url = \"https://drive.google.com/u/0/uc?export=download&confirm=HgGH&id=1nQDddS36y4AcJ87ocoMjyx46HGueiU6k\"\n", "output = 'airshowers.npz'\n", "\n", "if os.path.exists(output) == False:\n", " gdown.download(url, output, quiet=True)\n", "\n", "f = np.load(output)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Input 1: arrival times" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(200000, 9, 9)\n" ] } ], "source": [ "# time map\n", "T = f['time']\n", "T -= np.nanmean(T)\n", "T /= np.nanstd(T)\n", "T[np.isnan(T)] = 0\n", "\n", "print(T.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Plot four example arrival time maps" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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