MBTR.ipynb

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        "# Many Body Tensor Representation\n",
        "\n",
        "MBTR is a global descriptor for a molecule/unit cell. It eliminates rotational, translational, and permutation variances by gathering information about different configurations of $K$ atoms into tensors that are stratified by the involved chemical elements. All element combinations have an associated gaussian-smeared exponentially-weighted histogram.\n",
        "\n",
        "## The Tensor\n",
        "The tensor comprises of combinations of elements in different numbers. So, K1 is 1 element, K2 is 2 elements, and so on. These K's represent different expression of the molecule/unit-cell.\n",
        "\n",
        "### K1\n",
        "K1 represents the gaussian-smeared histogram for **counts** of each element type. So, in essense it is a matrix of size MxN, where M is the number of elements, and N is the number of bins.\n",
        "\n",
        "![K1](https://github.com/reinimaurer1/ML-CSC-tutorial/blob/master/images/k1.png?raw=1)\n",
        "\n",
        "### K2\n",
        "K2 represents the gaussian-smeared exponentially-weighted histogram **inverse distances** of pairs of elements. So, this becomes a tensor of size MxMxN, where M is the number of elements, and N is the number of bins.\n",
        "\n",
        "![K2](https://github.com/reinimaurer1/ML-CSC-tutorial/blob/master/images/k2.png?raw=1)\n",
        "\n",
        "### K3\n",
        "K3 represents the gaussian-smeared exponentially-weighted histogram **angles between triplets** of elements. So, this becomes a tensor of size MxMxMxN, where M is the number of elements, and N is the number of bins.\n",
        "\n",
        "![K3](https://github.com/reinimaurer1/ML-CSC-tutorial/blob/master/images/k3.png?raw=1)\n",
        "\n",
        "*Note: the dscribe package has implementation of MBTR up to K3*\n",
        "\n",
        "### K4 \n",
        "K4 represents the gaussian-smeared exponantially-weighted histogram **di-hedral angles** between quadruplets of elements. So, this becomes a tensor of size MxMxMxMxN, where M is the number of elements, and N is the number of bins.\n",
        "\n",
        "![K4](https://github.com/reinimaurer1/ML-CSC-tutorial/blob/master/images/k4.png?raw=1)\n",
        "\n",
        "## Weighting\n",
        "\n",
        "All the tensors, but K1, are weighted. This ensures that contributions from nearby atoms is higher, than from farther ones.\n",
        "\n",
        "For more info about MBTR see:\n",
        "[Huo, Haoyan, and Matthias Rupp. *arXiv preprint* **arXiv:1704.06439 (2017)**](https://arxiv.org/pdf/1704.06439.pdf)  \n",
        "\n",
        "For calculating MBTR, we use the [DScribe package](https://singroup.github.io/dscribe) as developed by [Surfaces and Interfaces at the Nanoscale, Aalto](http://physics.aalto.fi/en/groups/sin/)"
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      "source": [
        "## Example\n",
        "\n",
        "We are going to see MBTR in action for a simple NaCl system."
      ]
    },
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      "source": [
        "#resolve KRR dependency\n",
        "import os\n",
        "!pip install dscribe\n",
        "# --- INITIAL DEFINITIONS ---\n",
        "from dscribe.descriptors import MBTR\n",
        "import numpy as np\n",
        "from ase.visualize import view\n",
        "from ase import Atoms\n",
        "import matplotlib.pyplot as mpl"
      ],
      "execution_count": 2,
      "outputs": [
        {
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          "text": [
            "Collecting dscribe\n",
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            "Building wheels for collected packages: dscribe\n",
            "  Building wheel for dscribe (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for dscribe: filename=dscribe-1.1.0-cp37-cp37m-linux_x86_64.whl size=4339900 sha256=c003be1f68a6b409393cc1fe961cd6cca63c503de1cc3f37c36f9b75fca7dbd0\n",
            "  Stored in directory: /root/.cache/pip/wheels/05/f8/a6/c5328c447d56d1efed920c372cbd0086ac1e01de1b5adaa9db\n",
            "Successfully built dscribe\n",
            "Installing collected packages: sparse, pybind11, ase, dscribe\n",
            "Successfully installed ase-3.22.0 dscribe-1.1.0 pybind11-2.7.1 sparse-0.12.0\n"
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      "source": [
        "### Atom description\n",
        "\n",
        "We'll make an ase.Atoms class for NaCl"
      ]
    },
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        "colab": {
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      "source": [
        "# Define the system under study: NaCl in a conventional cell.\n",
        "NaCl_conv = Atoms(\n",
        "    cell=[\n",
        "        [5.6402, 0.0, 0.0],\n",
        "        [0.0, 5.6402, 0.0],\n",
        "        [0.0, 0.0, 5.6402]\n",
        "    ],\n",
        "    scaled_positions=[\n",
        "        [0.0, 0.5, 0.0],\n",
        "        [0.0, 0.5, 0.5],\n",
        "        [0.0, 0.0, 0.5],\n",
        "        [0.0, 0.0, 0.0],\n",
        "        [0.5, 0.5, 0.5],\n",
        "        [0.5, 0.5, 0.0],\n",
        "        [0.5, 0.0, 0.0],\n",
        "        [0.5, 0.0, 0.5]\n",
        "    ],\n",
        "    symbols=[\"Na\", \"Cl\", \"Na\", \"Cl\", \"Na\", \"Cl\", \"Na\", \"Cl\"],\n",
        ")\n",
        "view(NaCl_conv)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
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            "text/plain": [
              "<subprocess.Popen at 0x7f0bacd8e6d0>"
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            "tags": []
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          "execution_count": 3
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        "id": "MDGVGhQBg1ve"
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      "source": [
        "### Setting MBTR hyper-parameters\n",
        "\n",
        "Next we set-up hyper-parameters:\n",
        "1. species, the chemical elements to include in the MBTR, helps comparing two structures with missing elements\n",
        "2. k, list/set of K's to be computed\n",
        "3. grid: dictionary for K1, K2, K3 with\n",
        "    min, max: are the min and max values for each distribution\n",
        "    sigma, the exponent coefficient for smearing\n",
        "    n, number of bins.\n",
        "4. weights: dictionary of weighting functions to be used.\n",
        "\n",
        "**Note: The dscribe package has implementation of MBTR up to K3**\n"
      ]
    },
    {
      "cell_type": "code",
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        "colab": {
          "base_uri": "https://localhost:8080/"
        },
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        "outputId": "9e51553a-e11b-4b0a-b970-5a77e356c258"
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      "source": [
        "# Create the MBTR desciptor for the system\n",
        "mbtr = MBTR(\n",
        "    species=['Na', 'Cl'], # Na and Cl\n",
        "    periodic=True,\n",
        "    k1={\n",
        "        \"geometry\": { \"function\": \"atomic_number\" },\n",
        "        \"grid\": { \"min\": 10, \"max\": 18, \"sigma\": 0.1, \"n\": 200 },\n",
        "    },\n",
        "    k2={\n",
        "        \"geometry\": {\"function\": \"inverse_distance\"},\n",
        "        \"grid\": { \"min\": 0, \"max\": 0.7, \"sigma\": 0.01, \"n\": 200 },\n",
        "        \"weighting\": {\"function\": \"exp\", \"scale\": 0.75, \"cutoff\": 1e-3}\n",
        "    },\n",
        "    k3={\n",
        "        \"geometry\": {\"function\": \"cosine\"},\n",
        "        \"grid\": { \"min\": -1.0, \"max\": 1.0, \"sigma\": 0.05, \"n\": 200 },\n",
        "        \"weighting\": {\"function\": \"exp\", \"scale\": 0.5, \"cutoff\": 1e-3}\n",
        "    },\n",
        "    \n",
        "    flatten=False,\n",
        "    sparse=False)\n",
        "print(\"Number of features: {}\".format(mbtr.get_number_of_features()))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of features: 2200\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d41jgieXg1vh"
      },
      "source": [
        "### Calculate MBTR\n",
        "\n",
        "We call the create functin of mbtr class over our System(ase.Atoms) object"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3mJYol-ug1vj"
      },
      "source": [
        "#Create Descriptor\n",
        "desc = mbtr.create(NaCl_conv)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UHNybw62g1vk"
      },
      "source": [
        "### Plotting \n",
        "\n",
        "We will now plot all the tensors, in the same plot, for K1, K2, and K3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "tPlpW85pg1vl",
        "outputId": "b81c7a84-b7e2-429d-f914-64ee1d6d42cc"
      },
      "source": [
        "#plot K1\n",
        "x1 = mbtr.get_k1_axis()\n",
        "mpl.plot(x1, desc[\"k1\"][0, :], label=\"Na\", color=\"blue\")\n",
        "mpl.plot(x1, desc[\"k1\"][1, :], label=\"Cl\", color=\"orange\")\n",
        "mpl.ylabel(\"$\\phi$ (arbitrary units)\", size=14)\n",
        "mpl.xlabel(\"Atomic number\", size=14)\n",
        "mpl.title(\"The element count\", size=20)\n",
        "mpl.legend()\n",
        "mpl.show()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "-9811rwVg1vl",
        "outputId": "ee0ba2c6-99d8-4663-cc52-f941816ddab5"
      },
      "source": [
        "# Plot K2\n",
        "x2 = mbtr.get_k2_axis()\n",
        "mpl.plot(x2, desc[\"k2\"][0, 1, :], label=\"NaCl, ClNa\", color=\"blue\")\n",
        "mpl.plot(x2, desc[\"k2\"][1, 1, :], label=\"ClCl\", color=\"orange\")\n",
        "mpl.plot(x2, desc[\"k2\"][0, 0, :], label=\"NaNa\", color=\"green\")\n",
        "mpl.ylabel(\"$\\phi$ (arbitrary units)\", size=14)\n",
        "mpl.xlabel(\"Inverse distance (1/angstrom)\", size=14)\n",
        "mpl.title(\"Exponentially weighted inverse distance distribution\", size=20)\n",
        "mpl.legend()\n",
        "mpl.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 304
        },
        "id": "xV-US9dDg1vm",
        "outputId": "a3be16cf-2238-488c-dd10-30a10a0e231c"
      },
      "source": [
        "# Plot K3\n",
        "x3 = mbtr.get_k3_axis()\n",
        "mpl.plot(x3, desc[\"k3\"][0, 0, 0, :], label=\"NaNaNa, ClClCl\", color=\"blue\")\n",
        "mpl.plot(x3, desc[\"k3\"][0, 0, 1, :], label=\"NaNaCl, NaClCl\", color=\"orange\")\n",
        "mpl.plot(x3, desc[\"k3\"][1, 0, 1, :], label=\"NaClNa, ClNaCl\", color=\"green\")\n",
        "mpl.ylabel(\"$\\phi$ (arbitrary units)\", size=14)\n",
        "mpl.xlabel(\"cos(angle)\", size=14)\n",
        "mpl.title(\"Exponentially weighted angle distribution\", size=20)\n",
        "mpl.legend()\n",
        "mpl.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "voTWqEvzg1vm"
      },
      "source": [
        "## Remark\n",
        "\n",
        "The MBTR is a fingerprint of the entire system. Thus, it can be used to:\n",
        "1. Compare the similarity of two chemical system by taking comparing the MBTR values.\n",
        "2. Machine learn total properties, like energies, dipole moment, etc.\n",
        "\n",
        "## Exercise\n",
        "\n",
        "Verify that the MBTR is translationally and rotationally invariant."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gd4OF0QZg1vm"
      },
      "source": [
        "\n"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vi1t_XQ6iy1g"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}